Lab 3#
Imports#
from importlib import reload
import ARC_utilities
reload(ARC_utilities)
<module 'ARC_utilities' from '/mnt/c/Users/faust/OneDrive - UvA/teaching/ARC_course/arc-course/labs/ARC_utilities.py'>
from glob import glob
import json
from os import path
from pprint import pprint
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import numpy as np
import math
import matplotlib.gridspec as gridspec
import arckit
import arckit.vis as vis
from arckit.data import fmt_grid
import drawsvg
from ARC_utilities import plot_task, random_translate
from neural_utilities import extract_xml_answer, progress
from dotenv import load_dotenv, find_dotenv
import os
from openai import OpenAI
## copied from https://github.com/mxbi/arckit/issues/7
# Create a subclass of drawsvg.Group with a dummy embed_google_font method
class GroupWithFont(drawsvg.Group):
def embed_google_font(self, *args, **kwargs):
pass # Do nothing
# Monkey-patch drawsvg in the arckit.vis module
vis.drawsvg.Group = GroupWithFont
In this notebook, we go through three things:
Using the arckit library to display arc tasks (the examples in the repo’s readme don’t quite work).
Constructing a whole dataset from just a single task in a way that can be done at test time (what has been called ‘active inference’).
Using self-consistency prompting to improve accuracy - a good strategy for transduction.
Many more things would fit in this notebook, but as always time and energy are finite. I might add more if there’s interest - let me know!
Getting and manipulating the ARC tasks#
We can get all the tasks in a nice format using the arckit library:
train_set, eval_set = arckit.load_data()
Each task can be converted to a dictionary with keys ‘test’ and ‘train’, and with list of dictionaries are values. Each subdictionary has keys ‘input’ and ‘output’, and list of lists (representing the grids) as values. Here is an example:
eval_set.tasks[0].to_dict()
{'id': '00576224',
'train': [{'input': [[8, 6], [6, 4]],
'output': [[8, 6, 8, 6, 8, 6],
[6, 4, 6, 4, 6, 4],
[6, 8, 6, 8, 6, 8],
[4, 6, 4, 6, 4, 6],
[8, 6, 8, 6, 8, 6],
[6, 4, 6, 4, 6, 4]]},
{'input': [[7, 9], [4, 3]],
'output': [[7, 9, 7, 9, 7, 9],
[4, 3, 4, 3, 4, 3],
[9, 7, 9, 7, 9, 7],
[3, 4, 3, 4, 3, 4],
[7, 9, 7, 9, 7, 9],
[4, 3, 4, 3, 4, 3]]}],
'test': [{'input': [[3, 2], [7, 8]],
'output': [[3, 2, 3, 2, 3, 2],
[7, 8, 7, 8, 7, 8],
[2, 3, 2, 3, 2, 3],
[8, 7, 8, 7, 8, 7],
[3, 2, 3, 2, 3, 2],
[7, 8, 7, 8, 7, 8]]}]}
We can also use the arckit library to plot the grids. First, we load a task:
task = arckit.load_single('007bbfb7')
task.train[0]
(array([[0, 7, 7],
[7, 7, 7],
[0, 7, 7]]),
array([[0, 0, 0, 0, 7, 7, 0, 7, 7],
[0, 0, 0, 7, 7, 7, 7, 7, 7],
[0, 0, 0, 0, 7, 7, 0, 7, 7],
[0, 7, 7, 0, 7, 7, 0, 7, 7],
[7, 7, 7, 7, 7, 7, 7, 7, 7],
[0, 7, 7, 0, 7, 7, 0, 7, 7],
[0, 0, 0, 0, 7, 7, 0, 7, 7],
[0, 0, 0, 7, 7, 7, 7, 7, 7],
[0, 0, 0, 0, 7, 7, 0, 7, 7]]))
Then, we can plot a single grid:
grid = vis.draw_grid(task.train[0][1], xmax=3, ymax=3, padding=.5, label='Example')
grid
Or plot a whole task at once (very neat little library!):
task = vis.draw_task(train_set[0], width=20, height=8, label='Example', include_test=True)
task
You can get more information about what you can do with this library on their github page.
The accuracy on a task is the mean test-wise success, where a test prediction is successful if it is identical to the one produced by the transformation for the corresponding input. In the evaluation set, there’s only a handful of tasks with more than one test example; for those, task success can be != 1. or 0. Specifically, since they all have 2 test tasks, the accuracy can be 0.5.
arr = np.array([len(x['test']) for x in evaluation_data])
# print the number of examples for test tasks with more than one test example
arr[arr>1]
array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])
Active inference#
Once we have a task, we can “cross-augment” it in various ways to get many more examples (this was done e.g., by Akyürek et al. - see Lecture 5 for more discussion of this). This has two advantages. First, more data can help us train the system better in general. Second, if we construct the augmented dataset using simply the transformation examples from the test task, we can do this at test time on the tasks in the private set. This is useful because the concepts involved in the private set tasks might be a bit different from the ones that we can see in the public set!
Cross-augmentation#
Cross-augmentation refers to the Leave-One-Out procedure of constructing alternative tasks by taking the examples, removing one, and treating it as a test case with a known solution, which can then be used for fine-tuning.
task = arckit.load_single('007bbfb7')
This can be done quite quickly as follows, generating as many new subtasks as there are input-output examples:
example
{'input': [[2, 2, 2], [0, 0, 0], [0, 2, 2]],
'output': [[2, 2, 2, 2, 2, 2, 2, 2, 2],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 2, 2, 0, 2, 2, 0, 2, 2],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 2, 2, 2, 2, 2, 2],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 2, 2, 0, 2, 2]]}
train_task = task.to_dict()['train']
LOO_dataset = []
for i, example in enumerate(train_task):
train = train_task[:i]+train_task[i+1:]
LOO_dataset.append({
'task': arckit.Task('example', train, [example]),
'solution': example['output']
})
vis.draw_task(LOO_dataset[0]['task'], width=15, height=8, label='Example', include_test=True)
From here, you could collate each of these new subtasks into a 4-shot prompt with a known correct completion and use these prompts to fine tune an LLM on these additional problems, as we have done in the lab of module 4.
Exploiting invariances#
Something else that can be done to increase the training size at test time is to define a set of task-invariant transformations, which are likely to have the following property (given task-invariant transformation \(T\), task solution \(f\) and input \(i\)):
\[
\text{if } f(i) = o \text{, then } T(f(i)) = T(o)
\]
In other terms, we can generate a new example for the unknown task transformation by transforming both input and output in a known example. We can also compose the transformations and get even more transformations!
# let's take a single pair we're applying transformations on
pair = task.train[0]
apply_trans_to_pair = lambda t: lambda p: (t(p[0]), t(p[1]))
# let's take some of the transformations in Akyürek et al.
transformations = {
'Rot_90': lambda g: np.rot90(g, k=1), # 90 degrees clockwise
'Rot_180': lambda g: np.rot90(g, k=2), # 180 degrees
'Rot_270': lambda g: np.rot90(g, k=3), # 270 degrees (or -90)
'Flip_0': lambda g: np.flip(g, axis=1),
'Flip_1': lambda g: np.flip(g, axis=0),
'Refl_0r': lambda g: np.concatenate((np.flip(g, axis=1), g), axis=0),
'Refl_0': lambda g: np.concatenate((np.flip(g, axis=1), g), axis=1),
'Refl_1r': lambda g: np.concatenate((g, np.flip(g, axis=0)), axis=1),
'Refl_1': lambda g: np.concatenate((np.flip(g, axis=0), g), axis=1),
'RandTr_4': lambda g: random_translate(g, max_shift=4),
'Transp': lambda g: g.T,
'IncrWidth': lambda g: np.repeat(g, 2, axis=1),
'IncrRes': lambda g: np.repeat(g, 2, axis=0),
}
# little drawing helper function
def draw_pair(pair, transformations):
names = transformations.keys()
transf = transformations.values()
pairs = [
apply_trans_to_pair(t)(pair)
for t in transf
]
drawing = vis.draw_task(
arckit.Task(
'',
[{'input': p[0], 'output': p[1]} for p in pairs],
[]
),
width=40,
height=8,
)
drawing.extend( [
drawsvg.Text(n, font_size=0.4,x=i*(drawing.width/len(names)) + 1,y=-drawing.height/50)
for i,n in enumerate(names)
])
drawing.height = 11
return drawing
out = draw_pair(pair, transformations)
The basic thing to note here is that even without codifying the true task transformation, we are generating new examples of it by applying out transformations to both inputs and outputs. While the fact that these new examples are also instances of the same transformation might be obvious to us, it may not be obvious to the system we are training. And those transformations that the system does not find obvious might be precisely the ones needed to generalize the test input:
out.display_inline()
If we want to also apply multiple transformations at once, we are going to need a function that takes a list of functions and composes them together:
def chain(*func_list):
def chained(x):
for f in reversed(func_list):
x = f(x)
return x
return chained
For instance, we can compose the following \(\mathbb{N} \to \mathbb{N}\) functions, to get \(\lambda x: x*2 +1\):
f = chain(lambda x: x+1, lambda x: x*2)
print(f(1))
3
Now we can define some chained transformations:
# let's take some of the transformations in Akyürek et al.
composed_transformations = {
# flipping -> rotating vs. rotating -> flipping
'Flip0_Rot90': chain(transformations['Flip_0'], transformations['Rot_90']),
'Rot90_Flip0': chain(transformations['Rot_90'], transformations['Flip_0']),
# translate -> rotate vs. rotate -> translate
'RandTr4_Rot90': chain(transformations['RandTr_4'], transformations['Rot_90']),
'Rot90_RandTr4': chain(transformations['Rot_90'], transformations['RandTr_4']),
# A three-function chain example
'Rot90_Flip0_Transp': chain(transformations['Rot_90'], transformations['Flip_0'], transformations['Transp']),
# sometimes order doesn't matter!
'Refl0_IncrRes': chain(transformations['Refl_0'], transformations['IncrRes']),
'IncrRes_Refl0': chain(transformations['IncrRes'], transformations['Refl_0']),
}
out = draw_pair(pair, composed_transformations)
/home/fausto/mambaforge/envs/arccourse/lib/python3.11/site-packages/arckit/vis.py:147: RuntimeWarning: divide by zero encountered in divide
allocation[incr] += increment / incr.sum()
Note that the order of composition can matter, for instance if you flip and then rotate, you get a different result from first rotating and then flipping:
out
Can you hear the sound of group theory in the distance?
Voting systems: self-consistency prompting#
def get_prompt(task, i_test, spaces=True):
"""
Based on Task.gpt_prompt
"""
prompt = (
"We are playing a game which involves transforming an input grid of digits into an output grid of digits. "
"In general, digits form objects in 2D and the task is to perform some spatial transformation of these objects to go from the input grid to the output grid. "
"All the information about the transformation is contained within the input pairs themselves, "
"and your answer will only be correct if the output grid is exactly correct, so this is what I expect from you. "
"\n\nPlease answer with the following format:\n"
"<reasoning>\n...\n<\\reasoning>\n<answer>\nanswer grid\n<\\answer>\n\n"
"I will begin by giving you several examples of input-output pairs. "
"You will then be given a new input grid, and you must provide the corresponding output grid.\n\n"
)
i = 1
for inp, output in task.train:
prompt += f"Input {i}:\n{fmt_grid(inp, colour=False, spaces=spaces)}\nOutput {i}:\n{fmt_grid(output, colour=False, spaces=spaces)}\n\n"
i += 1
test_grid = task.test[i_test][0]
prompt += f"Input {i}:\n"
prompt += f"{fmt_grid(test_grid, colour=False, spaces=spaces)}"
return prompt
def draw_pairs(pairs, names):
drawing = vis.draw_task(
arckit.Task(
'',
[{'input': p[0], 'output': p[1]} for p in pairs],
[]
),
width=40,
height=8,
)
drawing.extend( [
drawsvg.Text(n, font_size=0.4,x=i*(drawing.width/len(names)),y=-drawing.height/50)
for i,n in enumerate(names)
])
drawing.height = 11
return drawing
Let’s implement the basic idea in Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, & Denny Zhou (2023). Self-Consistency Improves Chain of Thought Reasoning in Language Models. In The Eleventh International Conference on Learning Representations. Essentially we’re gonna produce a bunch of samples with reasoning and an answer and then pick the answer that was given most often!
task = arckit.load_single('007bbfb7')
prompt = get_prompt(task, 0)
This is what a prompt would look like:
print(prompt)
We are playing a game which involves transforming an input grid of digits into an output grid of digits. In general, digits form objects in 2D and the task is to perform some spatial transformation of these objects to go from the input grid to the output grid. All the information about the transformation is contained within the input pairs themselves, and your answer will only be correct if the output grid is exactly correct, so this is what I expect from you.
Please answer with the following format:
<reasoning>
...
<\reasoning>
<answer>
answer grid
<\answer>
I will begin by giving you several examples of input-output pairs. You will then be given a new input grid, and you must provide the corresponding output grid.
Input 1:
0 7 7
7 7 7
0 7 7
Output 1:
0 0 0 0 7 7 0 7 7
0 0 0 7 7 7 7 7 7
0 0 0 0 7 7 0 7 7
0 7 7 0 7 7 0 7 7
7 7 7 7 7 7 7 7 7
0 7 7 0 7 7 0 7 7
0 0 0 0 7 7 0 7 7
0 0 0 7 7 7 7 7 7
0 0 0 0 7 7 0 7 7
Input 2:
4 0 4
0 0 0
0 4 0
Output 2:
4 0 4 0 0 0 4 0 4
0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 4 0 4 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 4 0 0 0 0
Input 3:
0 0 0
0 0 2
2 0 2
Output 3:
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 2 0 2
0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 0 0 2
2 0 2 0 0 0 2 0 2
Input 4:
6 6 0
6 0 0
0 6 6
Output 4:
6 6 0 6 6 0 0 0 0
6 0 0 6 0 0 0 0 0
0 6 6 0 6 6 0 0 0
6 6 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0
0 6 6 0 0 0 0 0 0
0 0 0 6 6 0 6 6 0
0 0 0 6 0 0 6 0 0
0 0 0 0 6 6 0 6 6
Input 5:
2 2 2
0 0 0
0 2 2
Output 5:
2 2 2 2 2 2 2 2 2
0 0 0 0 0 0 0 0 0
0 2 2 0 2 2 0 2 2
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 2 2 2 2 2 2
0 0 0 0 0 0 0 0 0
0 0 0 0 2 2 0 2 2
Input 6:
7 0 7
7 0 7
7 7 0
And let’s ask gpt-4o to make some reasoned guesses:
n_samples = 30
confirmation = input("Running this will spend some $$. Do you want to run it anyway? (y/n): ").strip().lower()
if confirmation in ['y', 'yes']:
_ = load_dotenv('../../../../.openAI_env')
client = OpenAI(api_key=os.getenv('OPENAI-KEY'))
# more expensive but better!
model = "gpt-4o"
# cheapest model!
# model="gpt-4o-mini"
openai_data = []
out = display(progress(0, n_samples), display_id=True)
for i in range(n_samples):
completion = client.chat.completions.create(
model=model,
messages=[{"role": "user", "content": prompt}]
)
completion = completion.choices[0].message.content
print(completion)
openai_data.append({
'completion': completion,
'answer': extract_xml_answer(completion)
})
out.update(progress(i, n_samples))
with open(f'./{model}_openaidata.csv', 'w') as openfile:
json.dump(openai_data, openfile)
else:
print("You: 'In *this* economy?'")
<reasoning>
Analyzing the provided examples, it seems like the transformation follows a pattern where the input 3x3 grid is expanded into a 9x9 grid. Each cell in the input grid represents a 3x3 block in the output grid. The position of these blocks in the output follows a specific rule.
For a given digit in the input grid located at position (i, j), it will be represented by a 3x3 block located in specific positions of the 9x9 output grid based on (i, j).
Specifically:
- For Input 1 to Output 1:
- The "7" digits create a diagonal set of blocks in the output grid.
- In Input 2 to Output 2:
- The "4" digits form a similar pattern but occupy different positions forming diagonal blocks in a new configuration.
- The presence of 0s seems to result in empty blocks in corresponding locations in the 9x9 grid.
Following this pattern, from Input 6:
Given the Input 6 grid:
7 0 7
7 0 7
7 7 0
We'll use this understanding to identify which blocks will be formed in the output:
- The top-left 3x3 block and top-right 3x3 block should be filled with the digit "7".
- The middle-left 3x3 block and middle-right 3x3 block will also be filled with "7".
- The bottom-left and bottom-middle 3x3 blocks will be filled with "7".
In the 9x9 output grid, blocks are filled or empty based on their corresponding input grid digit.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 0 7 7 0 0 0
<\answer>
<reasoning>
The transformation involves taking the input 3x3 grid and replicating it into a larger 9x9 grid based on a specific pattern. The larger grid can be thought of as a 3x3 grid of 3x3 matrices, where each matrix is a copy or transformation of the input grid.
From the provided examples:
1. Each row of the enlarged grid is a concatenation of the input grid possibly with modifications (such as rotation or reflection).
2. The output grid often consists of the input grid repeated in specific rows matching the positions of non-zero digits in the initial input grid.
3. The alteration from input to output seems to involve mapping each non-zero element (such as a '7' or '4') onto all parts of a 3x3 tiling in the output.
Let's apply the same principles to Input 6:
Input 6:
```
7 0 7
7 0 7
7 7 0
```
We must replicate each part of the pattern to fit into a 9x9 grid, likely following the positional rules (or similar transformations) from the examples given.
Step-by-step reasoning:
- The element `7` at position (1,1) in the input will propagate throughout the output grid, maintaining its pattern as specified in the examples.
- Each section of 3 will stretch and take its position across the 3x3 sections of the output grid based on the pattern.
The pattern seems to align the given numbers into the grid without changing their locations but ensuring they fill in the appropriate 9x9 structure.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
<\answer>
<reasoning>
Each example involves a transformation of a 3x3 input grid into a 9x9 output grid. The examples suggest the transformation involves positioning the original 3x3 grid in different spots within the larger 9x9 grid, possibly rotated or flipped, but maintaining the main shapes. The new grid seems to be constructed by arranging the original 3x3 grid in different orientations and positions such that they form a larger symmetric pattern.
Analyzing the examples more deeply:
1. The output grid appears to be composed of 9 segments, each segment sized 3x3.
2. Across all examples, each segment in the 9x9 output mirrors some transformation of the original 3x3 input grid.
3. These transformations seem to involve rotations (90, 180, and 270 degrees) and possibly flips (horizontal/vertical).
For the task, I'll arrange the input grid in a pattern where the first square is the grid as is, the second is rotated 90 degrees, the third is the grid as is again, the fourth is vertically flipped, the fifth is rotated 180 degrees, the sixth is vertically flipped again, the seventh is the grid as is once more, the eighth is rotated 270 degrees, and the ninth is the grid as is again.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 0 0 0
0 7 7 7 0 7 7 0 7
0 0 0 7 7 0 7 0 7
0 0 0 7 0 7 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 7 7 0 7 0 7
7 7 0 7 0 7 7 7 0
<\answer>
<reasoning>
To solve this problem, we need to understand the transformation from a 3x3 input grid to a 9x9 output grid. The output grids exhibit a pattern of repetition and spatial arrangement that the input grid is transformed into.
Let's analyze the examples:
1. In Input 1, the number '7s' are arranged in a specific pattern that repeats in a grid pattern to fill the 9x9 grid.
2. A blank or zero space in the input translates to a larger area of zeros in the output.
3. Another observation is that the patterns appear to be rotated or mirrored in certain sections of the 9x9 output grid.
The transformation can be understood as follows for any given 3x3 grid:
- The 9x9 grid is divided into nine 3x3 segments.
- The input grid seems to be transposed or mirrored into those nine segments, such that:
- The first 3x3 segment (top-left) is a copy of the input.
- The second 3x3 (top-middle) could be a rotated/mirrored version, depending on observation.
- This transformation follows a specific pattern of symmetry or repetition established by the examples.
Thus, we need to establish the correct transformation base pattern for the specific input.
Let's apply this logic to transform Input 6:
Input 6:
```
7 0 7
7 0 7
7 7 0
```
- The input grid has a prominent diagonal and some zeros in between, and in Output 6, we can observe a symmetric repetition around the center.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
0 0 0 7 0 7 7 0 7
0 0 0 7 0 7 7 0 7
0 0 0 7 7 0 7 7 0
<\answer>
<reasoning>
In examining the transformation between input and output grids across the given examples, it appears that each 3x3 input grid maps into a 9x9 output grid. The transformation involves placing rotated or mirrored versions of the input grid pattern at multiple positions within the 9x9 matrix.
In each output grid:
1. The original 3x3 grid appears at four core locations forming the quadrants of the 9x9 grid. These four core positions are:
- Top-left (quadrant 1)
- Top-right (quadrant 2)
- Bottom-left (quadrant 3)
- Bottom-right (quadrant 4)
2. Additional reflections or rotations of the input grid are applied symmetrically around these core positions.
For the examples provided:
- In each quadrant, the grid cell (i, j) of the input appears in a fixed relationship within the 3x3 sub-grid of each quadrant. The pattern appears consistently in a mirrored or rotated fashion based on input values.
Following the pattern and mapping positions, I will apply a similar transformation to the new input grid.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
The transformation involves taking a 3x3 input grid and expanding it to a 9x9 output grid. Each "tile" in the input grid (3x3) corresponds to a "macro-tile" in the output grid (also 3x3), where the initial pattern repeats as needed.
To create the 9x9 output grid from a 3x3 input grid, each digit in the input grid is expanded into a 3x3 block in the output, effectively "blowing up" the grid by a factor of three.
For the given input (Input 6: 7 0 7; 7 0 7; 7 7 0), the pattern to be followed is observed from the previous exercises:
- For the first row:
- 7 becomes a 3x3 block of sevens,
- 0 becomes a 3x3 block of zeroes,
- 7 again becomes a block of sevens.
- This pattern applies to the entire grid: expanding and repeating the digits vertically and horizontally.
Constructing the output grid based on the above rules and patterns:
1. Top three rows entirely filled following the first row structure: "7 0 7".
2. Middle three rows replicate the entire pattern of the input grid.
3. Bottom three rows mirror the third row structure: "7 7 0".
<\reasoning>
<answer>
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 7 7 0 0 0 0
7 7 7 7 7 0 0 0 0
7 7 7 7 7 0 0 0 0
<\answer>
<reasoning>
Upon analyzing the previous input-output pairs, it appears that the transformation involves creating a 9x9 grid from the initial 3x3 grid. Each 3x3 input forms a centerpiece that is then reflected or arranged multiple times to fill a 9x9 block. This seems to follow a specific rule:
1. The 3x3 input grid is replicated to form a larger 9x9 output grid.
2. The pattern is repeated in distinct segments or blocks of the 9x9 grid, involving some symmetry or repetition of the 3x3 grid.
To solve Input 6, we reproduce and arrange it so that:
- It appears once without change in the specific positions that follow the pattern.
- It is reflected or translated according to the repetition scheme seen in previous examples.
Let's apply these observations to Input 6.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
<\answer>
<reasoning>
By examining the provided input-output pairs, we can deduce the transformation rule to apply to the input grid. Each input is a 3x3 grid, which is expanded into a 9x9 output grid.
Observing the transformations, the central idea is that each 3x3 input grid defines a block pattern repeated multiple times to form the larger 9x9 grid. For each input grid, the elements maintain their relative positions in different sections of the output grid.
The input grid is expanded into a 9x9 grid by positioning 3x3 copies of the original grid based on the following pattern:
1. The original 3x3 grid occupies the top-left 3x3 section and is then repeated at other specific sections of the 9x9 grid.
2. The pattern appears to involve a specific reflection/rotation scheme that creates symmetries in the output grid.
Given these observations, the task is to expand the 3x3 grid to form a 9x9 grid by repeating the original grid pattern while maintaining which positions will be filled based on predefined positions derived from the prior examples.
Now, applying this transformation rule to Input 6:
Input:
7 0 7
7 0 7
7 7 0
We can expand it into the 9x9 output grid by replicating this 3x3 structure strategically in each 3x3 sub-grid across the 9x9 grid:
- Place the original 3x3 grid in the top-left, middle row, and bottom-right 3x3 subsections of the 9x9 grid.
<\reasoning>
<answer>
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
0 0 0 7 0 7 7 0 7
0 0 0 7 0 7 7 0 7
0 0 0 7 7 0 7 7 0
0 0 0 0 0 0 7 0 7
0 0 0 0 0 0 7 0 7
0 0 0 0 0 0 7 7 0
<\answer>
<reasoning>
The task involves taking a 3x3 input grid and transforming it into a 9x9 output grid. The transformation follows a specific pattern observed from previous input-output pairs:
1. Each input grid maps to a 9x9 repeating grid where apparent segments of the 3x3 grid are repeated across the 9x9 grid.
2. The input 3x3 grid is placed into the 9x9 grid, occupying positions that resemble playing tic-tac-toe with three possible overlapping spots—the top-left, the center, and the bottom-right of the 9x9 grid.
3. Within the 9x9 grid, the original 3x3 grid idea replicates into each sector's position, mirroring the content and zeros elsewhere.
Using these observations, the transformation of a 3x3 grid [a b c; d e f; g h i] onto a 9x9 grid is deduced as:
```
a b c a b c a b c
d e f d e f d e f
g h i g h i g h i
a b c a b c a b c
d e f d e f d e f
g h i g h i g h i
a b c a b c a b c
d e f d e f d e f
g h i g h i g h i
```
Each 3x3 block corresponds to its respective position:
```
0 0 0
0 1 0
0 0 0
```
Where 1 is the repeating "block" spot laid over each of the nine 3x3 sectors.
This leads to the construction of the output grid as shown.
We'll apply this pattern to Input 6.
Input:
7 0 7
7 0 7
7 7 0
\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
Upon examining the provided examples, we observe that the transformation involves creating a 9x9 grid from the initial 3x3 input grid. The transformation seems to follow a mirrored pattern and replication involving the original grid elements. More specifically:
1. The input 3x3 grid is seemingly transformed into a 9x9 grid by replicating the rows and columns of the input with certain reflective patterns observed.
2. The strong diagonal of the new 9x9 grid usually resembles the diagonal of the input 3x3 grid.
3. Subsequent rows and columns show spatial mirroring around this diagonal, maintaining the orientation of digits.
4. In particular, the 3x3 input grid can be visualized as forming blocks within the 9x9 grid, with each block appearing as an embellished or mirrored section of the input.
We'll apply these inferred rules to transform the given Input 6 into its respective output.
Input 6 needs to be arranged following this pattern and mapping it into a larger grid while maintaining the orientation and apparent mirroring trends shown in the previous outputs:
- Replicate the input grid in several sections with changes in zeroes, positions, and orientations forming a final coherent grid pattern.
<\reasoning>
<answer>
Given the input:
7 0 7
7 0 7
7 7 0
The output according to the observed pattern is:
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 0 7 0
0 0 0 7 0 7 0 0 0
0 0 0 7 0 7 0 0 0
0 0 0 7 7 0 0 0 0
0 0 0 7 0 7 7 0 7
0 0 0 7 0 7 0 0 0
0 0 0 0 7 0 0 7 0
<\answer>
<reasoning>
From the given examples, the transformation involves constructing a larger 9x9 grid from the 3x3 input grid by overlaying multiple transformations of the input grid in a particular arrangement.
1. The input grid is expanded to three main 3x3 sections: the top, middle, and bottom sections of the output grid.
2. Each section (9x9 output grid) is created by placing the original 3x3 input grid at specific positions:
- The input grid is placed at the corners and mid-segments of the 9x9 grid.
- The arrangement involves both rotations and mirroring of the input grid to fill the 9x9 output grid.
3. Let's denote the input grid as I:
Example pattern placement for a hypothetical 9x9 grid:
```
I I I -> top
I I I -> middle
I I I -> bottom
```
Specific positioning and rotations/mirroring differs in each example.
Let's apply this pattern to Input 6.
Layout the grid:
```
7 0 7 | 7 0 7 | 7 0 7
7 0 7 | 7 0 7 | 7 0 7
7 7 0 | 7 7 0 | 7 7 0
7 0 7 | 7 0 7 | 7 0 7
7 0 7 | 7 0 7 | 7 0 7
7 7 0 | 7 7 0 | 7 7 0
7 0 7 | 7 0 7 | 7 0 7
7 0 7 | 7 0 7 | 7 0 7
7 7 0 | 7 7 0 | 7 7 0
```
- This involves stacking and potentially rotating the original grid to fill the entirety of the 9x9 output grid, creating a larger pattern that repeats sections of the input.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
Upon examining the input-output pairs, a consistent transformation pattern becomes apparent. Each input grid of 3x3 is expanded into a 9x9 grid in the output. This output grid is divided into nine 3x3 sub-grids, which are populated in a specific pattern based on the arrangement of the input grid:
1. The input 3x3 grid is placed in each 3x3 sub-grid of the 9x9 output in specific positions:
- The top-left, top-middle, and top-right sub-grids correspond directly to the input grid.
- The middle-left sub-grid is placed with the input grid shifted down by one position.
- The center sub-grid mirrors the original input.
- The middle-right sub-grid is also the input grid shifted down by one position.
- The bottom-left sub-grid has the input grid shifted right by one position.
- The bottom-center sub-grid is the input grid.
- The bottom-right sub-grid has the input grid shifted right by one position.
For Input 6, we will follow this discovered structure to populate the 9x9 grid.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
<\answer>
<reasoning>
The task involves transforming the input grid into a 3x3 grid replication in a larger 9x9 grid. Analyzing the given examples, the transformation operations are as follows:
1. The 3x3 input grid is repeated to form a 9x9 grid.
2. Each quadrant (3x3 section) of the 9x9 grid is either identical to the input or positioned with certain parts of the input.
Each 9x9 output grid derives from splitting it into nine 3x3 blocks. Let's consider each given example:
- **Example 1:**
Repeated pattern, with rotations or reflections such that the 4th, 6th, and final quadrants match input even though rotations.
- **Example 2 & Example 4:**
Quadrants differ by positions, derived from sets and empty generalized forms.
- **Example 5 & Example 3:**
Exhibit more direct replications from segments of the input.
#### Steps for transformation:
- Define nine 3x3 blocks from the input grid.
1. Replicate/transpose certain blocks based on variations.
2. Reflect certain sections that involve specific patterning.
Input 6:
7 0 7
7 0 7
7 7 0
Prepare 9x9 matrix upon studied patterns from previous outputs:
- Mirror blocks to need mirrored values.
- Maintain blocks with holding simple copies where the last quadrant constructs the diagonal.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 0 0 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
<\answer>
<reasoning>
The task involves transforming a small input grid into a larger 9x9 output grid following certain rules that can be deduced from given examples. The transformation pattern can be seen as replicating the 3x3 input pattern three times horizontally and vertically. Each entry in the input grid is represented three times in the same relative positions in the output grid.
Let's highlight the observed rules:
1. The input grid (3x3) is expanded into a 9x9 output grid.
2. The expansion seems to follow a tile-like pattern where each digit in the input grid is mapped into three equivalent positions in a row and column-wise manner in the output grid to form a larger pattern.
Given these rules, let's apply the transformation to Input 6:
- The top row '7 0 7' of the input becomes three rows in the output: '7 0 7 7 0 7 7 0 7'
- The second row '7 0 7' translates likewise.
- The third row '7 7 0' is repeated.
Thus the output grid should look like a tiling of the input grid's pattern, filling a 9x9 space.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
The task requires performing a specific transformation on a 3x3 input grid to produce a 9x9 output grid. From the examples provided, the transformation pattern can be deduced as follows:
1. Expand the 3x3 grid into a 9x9 grid by replicating each row of the input grid into three corresponding rows in the output grid and similarly replicate each column into three corresponding columns in the output grid.
2. Each number in the original grid influences its corresponding 3x3 section in the output grid.
For the given Input 6, the numbers in the input grid are:
- The first row is [7, 0, 7].
- The second row is [7, 0, 7].
- The third row is [7, 7, 0].
Expanding this into a 9x9 grid by repeating each number to create a 3x3 block:
- The first row [7, 0, 7] becomes a block of three rows: each '7' is expanded to a 3x3 block of '7's, and '0' is expanded to a 3x3 block of '0's.
- The same process is applied to the second and third rows.
This creates the following 9x9 grid:
<\reasoning>
<answer>
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
<\answer>
<reasoning>
Examining the examples, the transformation appears to be about expanding or repeating the input grid into a larger grid. Specifically, each input grid of size 3x3 is transformed into a 9x9 grid. This output grid is divided into nine 3x3 sub-grids corresponding to positions in a 3x3 layout (top-left, top-center, top-right, middle-left, center, middle-right, bottom-left, bottom-center, bottom-right).
Each sub-grid mirrors part of the input:
1. The input grid itself is expanded (or repeated) across specific positions of the 9x9 grid.
2. The positions correspond based on some pattern within a larger 3x3 block format.
3. Cells remain zero unless a mirrored part of the input grid corresponds to a filled value.
For Input 6:
1. Identify the blocks where non-zero numbers appear in the input.
2. Place those numbers in the corresponding locations of each of the 3x3 sub-grids within the 9x9 grid.
The pattern seems to maintain non-zero numbers in two ways:
- A digit in the input grid that is non-zero will appear wherever a digit exists in the corresponding output grid's position based on the position pattern established in previous examples, simulating diagonal repetition or symmetry.
Applying this understanding to Input 6, we identify that:
- The non-zero numbers in input positions overlap or mirror the sub-grid arrangements in the output at multiple positions.
Input 6:
7 0 7
7 0 7
7 7 0
From the pattern, we need to fill each 3x3 sub-grid in the output grid accordingly while ensuring diagonals with similar structures are populated with the input elements.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 0 7 0
0 0 0 7 0 7 0 0 0
0 0 0 7 0 7 0 0 0
0 0 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 0 7 0
<\answer>
<reasoning>
The task at hand involves determining how to transform a given 3x3 input grid into a larger 9x9 output grid. Examining the given examples reveals that the input grid pattern is replicated three times in each row and three times in each column of the output. This effect creates a 3x3 tiling pattern of the original grid, forming the larger grid.
To perform this transformation, each element of the original input grid appears in each respective position of each 3x3 subgrid within the 9x9 output. In both the subgrid and output, to fill out the entire 9x9 space, the input grid appears identical in each repetition.
Let's apply this understanding to Input 6:
1. Start with the original 3x3 matrix:
```
7 0 7
7 0 7
7 7 0
```
2. Replicate the entire grid pattern in a 3x3 arrangement to form a 9x9 grid:
- Each cell from the input grid should occupy three positions horizontally and three positions vertically in the resulting grid.
Following these steps, construct the 9x9 output grid:
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
By examining the examples, the transformation can be described as follows: The input grid is a 3x3 grid, and the output grid is a 9x9 grid. The transformation involves replicating the input grid multiple times in specific configurations to form the final 9x9 output grid.
1. The original 3x3 input grid is arranged into the 9x9 output grid.
2. The 9x9 grid is split into nine 3x3 sub-grids.
3. Each sub-grid configuration seems to have a distinct pattern for placement.
Upon investigating the examples given:
- The original input grid tends to occupy specific sub-grids across examples.
- The number positioning remains consistent with their original state in the input grid.
For Input 6 which is:
7 0 7
7 0 7
7 7 0
We'll place this input grid into the 9x9 output grid by following the patterns observed:
- The input grid mirrors itself into four corners of the 9x9 grid.
- The sub-grid at position [0,0], [0,3], [3,0], and [6,3] in the 9x9 grid is replaced with this input grid.
- Ensure correct placement of the modes by keeping track of positions in sub-grids.
<\reasoning>
<answer>
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
0 0 0 7 0 7 7 0 7
0 0 0 7 0 7 7 0 7
0 0 0 7 7 0 7 7 0
<\answer>
<reasoning>
Upon examining the provided examples of input and output grids, a transformation pattern can be established. The input grid is a 3x3 grid, and the output grid is consistently a 9x9 grid. This transformation seems to include the repetition of certain rows of the input grid across specific rows and columns of the 9x9 output grid.
Here's the transformation process:
1. Expand the input grid such that each number is represented multiple times in a larger 9x9 matrix.
2. Each row of the input grid is repeated three times in the rows and columns of the output grid to form specific submatrices.
3. The repetition follows this pattern:
- For row 1 of the input, fill rows 1-3 of the output by repeating the first row of the input three times across the columns.
- For row 2 of the input, fill the relevant segments of rows 4-6 of the output.
- For row 3 of the input, fill the relevant segments of rows 7-9 of the output.
Applying this to the given input grid "7 0 7; 7 0 7; 7 7 0":
1. First row "7 0 7" repeated across columns for output rows 1 to 3.
2. Second row "7 0 7" repeated across columns for output rows 4 to 6.
3. Third row "7 7 0" repeated across columns for output rows 7 to 9.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 7 0 7 7 0 7 7 0
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
The task involves transforming a 3x3 input grid into a 9x9 output grid, and the transformation appears to follow a specific pattern based on symmetry and repetition. Let's analyze the examples provided:
1. For each input grid, the non-zero digits seem to be arranged in a way that maintains the positions they occupy in their respective input sub-grids when mapped into various sections of the larger 9x9 grid.
2. Taking each input grid, it gets expanded into the 9x9 grid, with each 3x3 sub-grid in the 9x9 grid corresponding to the 3x3 input grid itself or a transformation of it, either by rotation, reflection, or direct mapping.
3. The output grid has the following structure:
- It's divided into 9 blocks of 3x3.
- Each block is a copy, either direct or transformed, of the input 3x3 matrix.
Analyzing these patterns, we notice:
- The transformation seems to replicate the structure by placing the 3x3 block appropriately in each of the 9 sections of the 9x9 grid, thus extending it.
4. From inputs and outputs:
- The input gets directly copied into the four corners and center of the 9x9 grid.
Therefore, for the input grid:
```
7 0 7
7 0 7
7 7 0
```
we follow the pattern identified:
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
0 0 0 7 0 7 0 0 0
0 0 0 7 0 7 0 0 0
0 0 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
<\answer>
<reasoning>
The transformation process evidently involves replicating and rearranging the elements of a 3x3 input grid into a new, larger 9x9 output grid. After analyzing the provided input-output pairs, the task seems to involve following specific patterns:
1. **Splitting each element into three parts and arranging them** - For each row in the input, these are repeated by the number of rows (3 for each input row) in the 9x9 grid.
2. **Distribution of input values** - Each triplet in the 3x3 grid contributes its part to a section of the output grid. This is repeated in horizontal and vertical sequences within the 9x9 grid.
By deconstructing the outputs in relation to their inputs:
- Each 3x3 set of numbers (in either rows or columns) is mapped in not direct, but predictable horizontal/vertical patterns in each section of the 9x9 grid.
- Given a line of three numbers, these numbers are spread into spaces across sections of the larger grid, maintaining relative positions but effectively duplicated or blanked out as needed.
Observations related to the specific transformation:
- Leading and trailing zeroes often extend, making them visibly larger blocks across the grid.
- The cross-sections formed by non-zero elements often retain distinct sub-patterns within each 3x3 section of the 9x9 grid based on their initial position.
The complexity mainly resides in determining when a specific number is set to repeat or remain empty based on its first appearance. In grid 6, new states should be observed and mapped by those same rules.
<\reasoning>
<answer>
7 0 7 7 0 0 7 0 7
7 0 7 7 0 0 7 0 7
7 7 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 0 0 0
7 0 7 7 0 0 7 0 7
7 0 7 7 0 0 7 0 7
7 7 0 7 7 0 0 0 0
<\answer>
<reasoning>
The task is to transform the given 3x3 input grid into a larger 9x9 output grid based on a pattern observed from the provided examples. Let's analyze the transformation process step-by-step:
1. **Repeat the Input Grid**:
The 3x3 input grid is repeated to expand it into a 9x9 grid, creating a matrix where the input grid occupies centered sections at various positions.
2. **Structure of the Output Grid**:
- The output grid consists of 9 smaller 3x3 grids.
- These grids replicate the 3x3 input grid in the original pattern, rotated or modified as needed.
3. **Pattern Identification**:
- For positions (1,1), (1,2), and (1,3), the top left repeats of input grids are placed.
- Similar patterns hold for middle and bottom sections: (2,1), (2,2), (2,3) for the middle, and (3,1), (3,2), (3,3) for the bottom rows.
With these observations, let's apply them to the given Input 6 to determine the Output 6:
Input 6:
7 0 7
7 0 7
7 7 0
Steps:
1. Identify that similar replication will appear, but each section might rotate or modify slightly.
2. Populate the initial top left (1,1) 3x3, replicate and pattern around with zeros to comply.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
0 0 0 7 0 7 0 0 0
0 0 0 7 0 7 0 0 0
0 0 0 7 7 0 0 0 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
<\answer>
<reasoning>
The task requires identifying a pattern or transformation applied to the input grid to produce the output grid. Upon examining the examples:
1. Each input grid is a 3x3 grid.
2. The resultant output grid is a 9x9 grid, which suggests that each cell in the 3x3 grid is expanded into a 3x3 block in the output grid.
3. The input digit dictates the composition of its corresponding 3x3 block in the output:
- A digit (non-zero) in the input grid becomes a 3x3 matrix filled with the same digit in the output grid.
- A zero in the input grid results in a 3x3 block filled with zeros in the output grid.
4. Each input grid cell's upper-left corner's position is used as the reference point to place its corresponding 3x3 block in the output grid.
Utilizing these observations, we can transform the new input into the expected output by repeating the transformation seen in previous examples.
Applying this knowledge to Input 6:
1. The input grid is:
```
7 0 7
7 0 7
7 7 0
```
2. Transform each digit into a 3x3 block:
- Digit '7' becomes:
```
7 7 7
7 7 7
7 7 7
```
- Digit '0' becomes:
```
0 0 0
0 0 0
0 0 0
```
3. The resulting output grid is constructed by replacing each cell in the input grid with its corresponding 3x3 block. The position of each 3x3 block corresponds to the same rows and columns as the input grid but expanded by a factor of 3.
<\reasoning>
<answer>
```
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
```
<\answer>
<reasoning>
The transformation observed in the previous examples involves a rotation and repetition of the input grid digits in a 9x9 output grid. Specifically, the input grid appears to be repeated in a 3x3 formation for a 9x9 output, with certain transformations such as rotation applied. Let us break this down further:
1. **Rotation and Placement:**
- The input grid seems to be rotated or transformed in certain instances before repetition.
- The repetition has a pattern: the input grid is repeated three times in each dimension to form the 9x9 output.
2. **Observation of Patterns:**
- Input patterns are reused without any changes for some examples, while in others, the patterns are mirrored or rotated.
- Observing the provided examples:
- Example 1 and 4 involve repeating the grid without rotation.
- Example 2 and 3 involve repeating, with some parts rotated or transformed (mostly mirroring or positioning transformation).
- Example 5 involves repeating without transformation.
For the current input grid (Input 6), the grid is:
```
7 0 7
7 0 7
7 7 0
```
The transformation can be deduced by examining the specific placement and transformation rules applied to previous grids. The pattern suggested is direct repetition implying replication with unchanged orientation to form the 9x9 matrix. Let's apply this to create the potential solution:
- Row 1 of the grid {{7, 0, 7}} is repeated on positions [1, 4, 7] across the row, forming [7, 0, 7, 7, 0, 7, 7, 0, 7].
- Repeat this for the subsequent rows of the grid to fill:
- Rows 2 and 3 in the output with similar structure maintaining the pattern but moved down 3 or 6 spaces.
<\reasoning>
<answer>
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 7 0 7 7 0
<\answer>
<reasoning>
The transformation task involves taking the input 3x3 grid and converting it into a 9x9 grid. The transformation pattern observed from the examples can be summarized as follows:
1. The 3x3 input grid is used to generate a 9x9 output grid by placing each input element at a specific position in the output grid. Specifically, the input grid is "exploded" into nine 3x3 sub-grids based on original positioning, while maintaining the relative arrangement.
2. Each cell (i, j) from the input grid appears as a 3x3 sub-grid within the larger 9x9 grid in a specific pattern:
- The input cell at (0, 0) appears as a 3x3 sub-grid at top-left corner (0,0) of the 9x9 grid.
- The input cell at (0, 1) appears as a 3x3 sub-grid centered horizontally in the top row (0,3).
- The input cell at (0, 2) appears as a 3x3 sub-grid at top-right corner (0,6).
- Similarly for the next rows where each cell is assigned its 3x3 sub-grid in a corresponding pattern.
3. If the input cell contains a non-zero digit, the corresponding 3x3 sub-grid is filled entirely with the same digit. If it contains zero, it results in a sub-grid that remains filled with zeroes.
Applying the above pattern to "Input 6":
- At position (0,0) in the input, we have the value 7, so (0,0)-(2,2) in the output grid is filled with 7.
- At position (0,1), value is 0, so fill (0,3)-(2,5) in the output with 0.
- At position (0,2), value is 7, fill (0,6)-(2,8) with 7.
- At position (1, 0), value is 7, fill (3,0)-(5,2) with 7.
- At position (1, 1), value is 0, fill (3,3)-(5,5) with 0.
- At position (1, 2), value is 7, fill (3,6)-(5,8) with 7.
- At position (2, 0), value is 7, fill (6,0)-(8,2) with 7.
- At position (2, 1), value is 7, fill (6,3)-(8,5) with 7.
- At position (2, 2), value is 0, fill (6,6)-(8,8) with 0.
<\reasoning>
<answer>
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 0 0 0 7 7 7
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
7 7 7 7 7 7 0 0 0
<\answer>
<reasoning>
The task is to transform an input grid of digits into a new 9x9 output grid. The transformation appears to involve rotating the input grid in 90-degree intervals and placing these rotations in separate quadrants of a 9x9 grid, as well as reproducing the original grid in certain quadrants. From the analysis of previous input and output grid pairs, we can identify a pattern:
1. The input grid rotates 90 degrees clockwise, 180 degrees, and 270 degrees, filling the different corners of the 9x9 grid.
2. The original grid also appears in specific places, sometimes central or repeated in different locations, possibly with some overlap.
3. The remaining elements in the 9x9 grid are filled with zeros.
Let’s apply this transformation logic to Input 6. The input is:
```
7 0 7
7 0 7
7 7 0
```
We will rotate this grid:
- 90 degrees clockwise:
```
7 7 7
7 0 0
0 7 7
```
- 180 degrees:
```
0 7 7
7 0 7
7 0 7
```
- 270 degrees clockwise:
```
7 7 0
0 0 7
7 7 7
```
Now, place these transformed grids into a 9x9 grid while preserving some parts of the original as in previous examples. Based on the prior patterns, replicate the original grid at multiple quadrants and fill with zeros where necessary.
<\reasoning>
<answer>
Output 6 is:
```
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 0 7 7
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 0 7 7 0 0 0
0 0 0 7 0 7 7 0 7
0 0 0 7 0 7 7 0 7
0 0 0 0 7 7 7 7 0
```
<\answer>
<reasoning>
For the given pattern transformation, we can observe a consistent modification in how the input grid is expanded into an output grid. Specifically, a 3x3 input grid is expanded into a 9x9 output grid in a specific way.
The transformation essentially involves taking each row and column from the 3x3 input and expanding it into the corresponding block of the 9x9 output.
To better understand how this mapping is realized, observe the following:
1. Each row from the input grid becomes repeated three times in the corresponding 3-row section of the output grid. However, the repetition will shift based on the original position of non-zero elements in the input grid.
2. Each column in the output block likewise mirrors this repetition structure, influenced by the input column positions.
3. First Row Mapping:
- Input (Row 1): 7 0 7
- Output Rows (1-3, Columns): Maps Row 1 on [1:3, 1:3], shifts are zeroed in accordance to the gaps in zero positions.
4. Second Row Mapping:
- Input (Row 2): 7 0 7
- Output Rows (4-6, Columns): Maps Row 2 on [4:6, 1:3], repetition follows, with zero blocks added where zeroed in input.
5. Third Row Mapping:
- Input (Row 3): 7 7 0
- Output Rows (7-9,Columns): Maps Row 2 [7:9,1:3].
Essentially, each digit in the input grid impacts a 3x3 block within the output grid. This method divides these transformations into clear segments.
<\reasoning>
<answer>
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 0 7 7 0 7 0 0 0
7 7 0 7 7 0 0 0 0
7 7 0 7 7 0 0 0 0
7 7 0 7 7 0 0 0 0
<\answer>
<reasoning>
To determine the transformation rule from the given examples, let's analyze each input-output pair:
- In each case, the input grid is 3x3, and the output grid is 9x9.
- To create a 9x9 output grid from a 3x3 input grid, we are replicating the input grid to fill a 3x3 grid of 3x3 matrices, resulting in a 9x9 matrix.
Here is the step-by-step process:
1. The top-left 3x3 section of the output grid is a copy of the input grid.
2. The top-center 3x3 section is the input grid with columns shifted left by 1.
3. The top-right 3x3 section is the input grid with columns shifted left by 2.
4. The middle-left 3x3 section is the input grid with rows shifted up by 1.
5. The middle-center 3x3 section is 0s (assuming zero padding or an empty state).
6. The middle-right 3x3 section is the input grid with rows shifted up by 1 and columns shifted left by 2.
7. The bottom-left 3x3 section is the input grid with rows shifted up by 2.
8. The bottom-center 3x3 section has columns shifted left by 1 and rows shifted up by 2.
9. The bottom-right 3x3 section is a diagonal reflection of the input grid, indicating possibly a mirror effect diagonally.
Now let's apply these observations to Input 6:
Input 6:
7 0 7
7 0 7
7 7 0
Let's apply the transformation logic to generate the output for Input 6.
<\reasoning>
<answer>
7 0 7 0 7 0 7 0 7
7 0 7 0 7 0 7 0 7
7 7 0 7 7 0 7 7 0
0 7 0 7 0 7 0 7 0
0 0 0 0 0 0 0 0 0
7 0 0 0 7 0 0 0 7
0 7 7 7 0 7 7 0 7
0 0 7 0 0 7 0 0 0
7 0 7 7 0 7 7 0 0
<\answer>
<reasoning>
Observing the given input-output pairs, it seems the transformation involves creating a larger grid (9x9) from the smaller input grid (3x3). Let's investigate the pattern.
Each 3x3 grid is expanded into a 9x9 grid by replicating patterns within 3 subsets:
1. Input 3x3 patterns are placed in their original form in specific positions, with zeros filling other positions.
2. These positions vary based on their original position in the 3x3 grid, making a larger composite grid.
3. Each digit in the 3x3 grid creates a distinct pattern in the final 9x9 grid, distributed across different 3x3 sections.
By reviewing the previous examples, the digits appear in the new grid as follows:
- The top-left segment of the 9x9 grid replicates the original 3x3 grid with each non-zero element.
- Other segments also take turns representing 3x3 parts of the input grid, moving these around the larger array in a way that maintains overall symmetry and pattern transformation.
For Input 6, we analyze it and create a larger grid by mapping zeros and non-zero numbers accordingly, repeating the pattern similar to others.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
0 0 0 7 0 7 0 0 0
0 0 0 7 0 7 0 0 0
0 0 0 7 7 0 0 0 0
0 0 0 7 0 7 7 0 0
0 0 0 7 0 7 7 0 0
0 0 0 7 7 0 0 0 0
<\answer>
<reasoning>
From observing the input-output pairs, it is evident that each 3x3 input grid is transformed into a 9x9 output grid. The transformation involves replicating the input grid in specific sections of the output grid. The structure of the output grid seems to follow a certain pattern based on the arrangement of non-zero digits in the input grid.
Looking at the input-output pairs:
1. For Input 1, the digit '7' is prominent and replicates across the 9x9 grid with the center cluster being filled completely.
2. In Input 2, the digit '4' appears to be mirrored and replicated in specific spots while the rest is filled with zeros.
3. Input 3 shows a diagonal pattern created by the digit '2'.
4. Input 4 has a mirrored L-shape pattern for the digit '6'.
5. Input 5 exhibits a full horizontal line of '2's replicated in the middle rows.
The transformations likely depend on the input grid's pattern, concentrating or repeating non-zero values in distinct mirrored or linear arrangements in the output grid.
For Input 6, the input grid is:
7 0 7
7 0 7
7 7 0
Following the previously discerned pattern:
- The first row [7 0 7] implies a repetition of 7 on the sides and zeroes in between.
- The second row is similar, with 7s on the sides and zeroes, suggesting continuity of the same pattern.
- The last row [7 7 0] could indicate an increase in density for the zeros towards the end and more concentration of 7s on the top left and mirrored to the bottom.
Thus, in replicating the pattern based on non-zero digits, the anticipated transformation mimics those prominent digit lines horizontally, vertically, diagonally, or in L-shapes, depending on which cluster of digits appears more concentrated.
<\reasoning>
<answer>
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 0 0 0 7 0 7
7 0 7 0 0 0 7 0 7
7 7 0 0 0 0 7 7 0
7 0 7 7 0 7 7 0 7
7 0 7 7 0 7 7 0 7
7 7 0 7 0 7 7 7 0
<\answer>
I’ve already one this - let’s just load the file:
with open(f'./{model}_openaidata.csv', 'rb') as openfile:
openai_data = json.load(openfile)
And now let’s count each time the model gave each answer:
unique, unique_counts = np.unique([x['answer'] for x in openai_data], return_counts=True)
formatted = []
for x, count in zip(unique, unique_counts):
try:
sub = []
for y in x.split('\n')[:-1]:
sub.append([int(j) for j in y.split()])
formatted.append({'count': count, 'value': sub})
except:
print("didn't work")
didn't work
didn't work
didn't work
formatted
[{'count': 1,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 0, 7, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 0, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 7, 0, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 7, 0, 0],
[0, 0, 0, 7, 0, 7, 7, 0, 0],
[0, 0, 0, 7, 7, 0, 0, 0, 0]]},
{'count': 2,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 0, 0, 0],
[0, 0, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 0, 7, 7, 0, 0, 0]]},
{'count': 1,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 0, 7, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 7, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 0, 7, 0, 7, 0, 7],
[7, 0, 7, 0, 7, 0, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[0, 7, 0, 7, 0, 7, 0, 7, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[7, 0, 0, 0, 7, 0, 0, 0, 7],
[0, 7, 7, 7, 0, 7, 7, 0, 7],
[0, 0, 7, 0, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 0, 7, 0, 7],
[7, 0, 7, 7, 0, 0, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 0, 0, 0],
[7, 0, 7, 7, 0, 0, 7, 0, 7],
[7, 0, 7, 7, 0, 0, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 0, 0, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 7, 0, 7, 7, 0],
[0, 0, 0, 0, 0, 0, 7, 0, 7],
[0, 0, 0, 0, 0, 0, 7, 0, 7],
[0, 0, 0, 0, 0, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 7, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 7, 0, 7, 7, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[0, 7, 7, 7, 0, 7, 7, 0, 7],
[0, 0, 0, 7, 7, 0, 7, 0, 7],
[0, 0, 0, 7, 0, 7, 7, 7, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 7, 7, 0, 7, 0, 7],
[7, 7, 0, 7, 0, 7, 7, 7, 0]]},
{'count': 3,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 0, 0, 0],
[7, 7, 0, 7, 7, 0, 0, 0, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0]]},
{'count': 5,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 0, 7, 7, 0, 7, 7, 0, 7],
[7, 7, 0, 7, 7, 0, 0, 0, 0],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 0, 7, 0, 0, 0, 7, 0, 7],
[7, 7, 0, 0, 0, 0, 7, 7, 0]]},
{'count': 1,
'value': [[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 7, 7, 0, 0, 0, 0],
[7, 7, 7, 7, 7, 0, 0, 0, 0],
[7, 7, 7, 7, 7, 0, 0, 0, 0]]},
{'count': 2,
'value': [[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 0, 0, 0, 7, 7, 7],
[7, 7, 7, 7, 7, 7, 0, 0, 0],
[7, 7, 7, 7, 7, 7, 0, 0, 0],
[7, 7, 7, 7, 7, 7, 0, 0, 0]]}]
len([f'Count: {x}' for x in unique_counts])
22
len([(task.test[0][0], x['value']) for x in formatted])
19
draw_pairs([(task.test[0][0], x['value']) for x in formatted], [f'Count: {x["count"]}' for x in formatted])
It didn’t work out in this case, but that’s how it works - Try it with other examples!