o1, 2024-dec-17

---

### Preamble
You are an expert in ARC (Abstraction & Reasoning Corpus).

You are also an LLM so tokenization may impact how you see the image.
for example three zeros may be just a single token, or it may be multiple tokens.
for example the color 'blue' may be just a single token, or it may be multiple tokens.
You cannot assume that the image you perceive is correct due to the tokenization.
For this reason multiple representations are provided, so you can better reason about the puzzle.

Be aware about of keeping the number of response tokens fairly short, to minimize energy consumption.
In your response, please don't repeat one of the input images, since it's already in the prompt. It's a waste of tokens.
If you need to refer to a particular image, then write what transformation N input/output -> representation name.



Regarding "representation RLE".
This algorithm applies run-length encoding (RLE) to images, reducing sequences of identical pixels to shorter symbolic forms. 
It starts by noting the image's width and height, then processes each line. If an entire line is the same color, it writes that color once. 
Otherwise, it breaks the line into consecutive runs of identical pixels, using letters `a` through `z` to represent runs of lengths 2 to 27, 
followed by the color. Single pixels are just written as their color value. When a line repeats the previous one, it's marked with a comma only. 
This yields a concise, text-based compression.



Use a likert scale for your confidence level.
Strongly negative, weakly negative, medium, weakly positive, strongly positive.
Whenever there is an observation you are making, please write it down with your confidence level about it.
Be mindful of overstating confidence, especially in complex tasks like ARC, where multiple transformations might coexist.


- Observe first, assume cautiously, generalize carefully.
- Cross-check rigorously and revise judgments as needed.
- Treat confidence as a flexible tool, not a static declaration.


Check for Overfitting
Consider whether the observed pattern is just a coincidence or if it can be explained by a simpler rule.
For example, if the transformations are consistent with adding red pixels at symmetrical locations or at
positions defined by the coordinates of the blue pixels. Or some other color or pattern.


# The ARC puzzle

## Train Pair 0 Input

- width: 10
- height: 10
- number_of_unique_colors: 2
- most popular color: (0 black ⚫)
- least popular color: (1 blue 🔵)
- color (0 black ⚫), count 72
- color (1 blue 🔵), count 28


representation: digits
```
1110000000
1010000100
1110001110
0000000100
0100000000
1110000000
0101110000
0001010011
0001110000
0000000000
```


representation: color names
```
blue blue blue black black black black black black black
blue black blue black black black black blue black black
blue blue blue black black black blue blue blue black
black black black black black black black blue black black
black blue black black black black black black black black
blue blue blue black black black black black black black
black blue black blue blue blue black black black black
black black black blue black blue black black blue blue
black black black blue blue blue black black black black
black black black black black black black black black black
```


representation: Excel
```
,A,B,C,D,E,F,G,H,I,J
1,1,1,1,0,0,0,0,0,0,0
2,1,0,1,0,0,0,0,1,0,0
3,1,1,1,0,0,0,1,1,1,0
4,0,0,0,0,0,0,0,1,0,0
5,0,1,0,0,0,0,0,0,0,0
6,1,1,1,0,0,0,0,0,0,0
7,0,1,0,1,1,1,0,0,0,0
8,0,0,0,1,0,1,0,0,1,1
9,0,0,0,1,1,1,0,0,0,0
10,0,0,0,0,0,0,0,0,0,0
```


representation: emoji
```
🔵🔵🔵⚫⚫⚫⚫⚫⚫⚫
🔵⚫🔵⚫⚫⚫⚫🔵⚫⚫
🔵🔵🔵⚫⚫⚫🔵🔵🔵⚫
⚫⚫⚫⚫⚫⚫⚫🔵⚫⚫
⚫🔵⚫⚫⚫⚫⚫⚫⚫⚫
🔵🔵🔵⚫⚫⚫⚫⚫⚫⚫
⚫🔵⚫🔵🔵🔵⚫⚫⚫⚫
⚫⚫⚫🔵⚫🔵⚫⚫🔵🔵
⚫⚫⚫🔵🔵🔵⚫⚫⚫⚫
⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫
```


representation: python dictionary
```python
{'width':10,'height':10,'background':0,(0,0):1,(1,0):1,(2,0):1,(0,1):1,(2,1):1,(7,1):1,(0,2):1,(1,2):1,(2,2):1,(6,2):1,(7,2):1,(8,2):1,(7,3):1,(1,4):1,(0,5):1,(1,5):1,(2,5):1,(1,6):1,(3,6):1,(4,6):1,(5,6):1,(3,7):1,(5,7):1,(8,7):1,(9,7):1,(3,8):1,(4,8):1,(5,8):1}
```


representation: RLE
```
10 10 b1f0,101c01a0,b1b0b10,f01a0,01g0,b1f0,010b1c0,b0101a0a1,b0b1c0,0
```


representation: RLE transposed
```
10 10 b1a01c0,1010b1b0,b1a01c0,e0b10,e01010,e0b10,a01f0,0b1e0,a01c01a0,f01a0
```


## Train Pair 0 Output

- width: 10
- height: 10
- number_of_unique_colors: 3
- most popular color: (0 black ⚫)
- least popular color: (2 red 🔴)
- color (0 black ⚫), count 78
- color (1 blue 🔵), count 12
- color (2 red 🔴), count 10


representation: digits
```
0200000000
2220000100
0200001110
0000000100
0100000000
1110000000
0100200000
0002220011
0000200000
0000000000
```


representation: color names
```
black red black black black black black black black black
red red red black black black black blue black black
black red black black black black blue blue blue black
black black black black black black black blue black black
black blue black black black black black black black black
blue blue blue black black black black black black black
black blue black black red black black black black black
black black black red red red black black blue blue
black black black black red black black black black black
black black black black black black black black black black
```


representation: Excel
```
,A,B,C,D,E,F,G,H,I,J
1,0,2,0,0,0,0,0,0,0,0
2,2,2,2,0,0,0,0,1,0,0
3,0,2,0,0,0,0,1,1,1,0
4,0,0,0,0,0,0,0,1,0,0
5,0,1,0,0,0,0,0,0,0,0
6,1,1,1,0,0,0,0,0,0,0
7,0,1,0,0,2,0,0,0,0,0
8,0,0,0,2,2,2,0,0,1,1
9,0,0,0,0,2,0,0,0,0,0
10,0,0,0,0,0,0,0,0,0,0
```


representation: emoji
```
⚫🔴⚫⚫⚫⚫⚫⚫⚫⚫
🔴🔴🔴⚫⚫⚫⚫🔵⚫⚫
⚫🔴⚫⚫⚫⚫🔵🔵🔵⚫
⚫⚫⚫⚫⚫⚫⚫🔵⚫⚫
⚫🔵⚫⚫⚫⚫⚫⚫⚫⚫
🔵🔵🔵⚫⚫⚫⚫⚫⚫⚫
⚫🔵⚫⚫🔴⚫⚫⚫⚫⚫
⚫⚫⚫🔴🔴🔴⚫⚫🔵🔵
⚫⚫⚫⚫🔴⚫⚫⚫⚫⚫
⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫
```


representation: python dictionary
```python
{'width':10,'height':10,'background':0,(1,0):2,(0,1):2,(1,1):2,(2,1):2,(7,1):1,(1,2):2,(6,2):1,(7,2):1,(8,2):1,(7,3):1,(1,4):1,(0,5):1,(1,5):1,(2,5):1,(1,6):1,(4,6):2,(3,7):2,(4,7):2,(5,7):2,(8,7):1,(9,7):1,(4,8):2}
```


representation: RLE
```
10 10 02g0,b2c01a0,02c0b10,f01a0,01g0,b1f0,01a02d0,b0b2a0a1,c02d0,0
```


representation: RLE transposed
```
10 10 02b01c0,b20b1b0,02b01c0,f02a0,e0b20,f02a0,a01f0,0b1e0,a01c01a0,f01a0
```


## Train Pair 1 Input

- width: 10
- height: 10
- number_of_unique_colors: 2
- most popular color: (0 black ⚫)
- least popular color: (1 blue 🔵)
- color (0 black ⚫), count 71
- color (1 blue 🔵), count 29


representation: digits
```
0000111000
1100101000
1100111000
0000000010
0000000111
0111000010
0101000000
0111001000
0000001110
0000000000
```


representation: color names
```
black black black black blue blue blue black black black
blue blue black black blue black blue black black black
blue blue black black blue blue blue black black black
black black black black black black black black blue black
black black black black black black black blue blue blue
black blue blue blue black black black black blue black
black blue black blue black black black black black black
black blue blue blue black black blue black black black
black black black black black black blue blue blue black
black black black black black black black black black black
```


representation: Excel
```
,A,B,C,D,E,F,G,H,I,J
1,0,0,0,0,1,1,1,0,0,0
2,1,1,0,0,1,0,1,0,0,0
3,1,1,0,0,1,1,1,0,0,0
4,0,0,0,0,0,0,0,0,1,0
5,0,0,0,0,0,0,0,1,1,1
6,0,1,1,1,0,0,0,0,1,0
7,0,1,0,1,0,0,0,0,0,0
8,0,1,1,1,0,0,1,0,0,0
9,0,0,0,0,0,0,1,1,1,0
10,0,0,0,0,0,0,0,0,0,0
```


representation: emoji
```
⚫⚫⚫⚫🔵🔵🔵⚫⚫⚫
🔵🔵⚫⚫🔵⚫🔵⚫⚫⚫
🔵🔵⚫⚫🔵🔵🔵⚫⚫⚫
⚫⚫⚫⚫⚫⚫⚫⚫🔵⚫
⚫⚫⚫⚫⚫⚫⚫🔵🔵🔵
⚫🔵🔵🔵⚫⚫⚫⚫🔵⚫
⚫🔵⚫🔵⚫⚫⚫⚫⚫⚫
⚫🔵🔵🔵⚫⚫🔵⚫⚫⚫
⚫⚫⚫⚫⚫⚫🔵🔵🔵⚫
⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫
```


representation: python dictionary
```python
{'width':10,'height':10,'background':0,(4,0):1,(5,0):1,(6,0):1,(0,1):1,(1,1):1,(4,1):1,(6,1):1,(0,2):1,(1,2):1,(4,2):1,(5,2):1,(6,2):1,(8,3):1,(7,4):1,(8,4):1,(9,4):1,(1,5):1,(2,5):1,(3,5):1,(8,5):1,(1,6):1,(3,6):1,(1,7):1,(2,7):1,(3,7):1,(6,7):1,(6,8):1,(7,8):1,(8,8):1}
```


representation: RLE
```
10 10 c0b1b0,a1a0101b0,a1a0b1b0,g010,f0b1,0b1c010,0101e0,0b1a01b0,e0b10,0
```


representation: RLE transposed
```
10 10 0a1f0,0a1a0b1a0,d0101a0,d0b1a0,b1f0,101f0,b1c0a10,c01b010,b0b1a010,c01d0
```


## Train Pair 1 Output

- width: 10
- height: 10
- number_of_unique_colors: 3
- most popular color: (0 black ⚫)
- least popular color: (2 red 🔴)
- color (0 black ⚫), count 77
- color (1 blue 🔵), count 13
- color (2 red 🔴), count 10


representation: digits
```
0000020000
1100222000
1100020000
0000000010
0000000111
0020000010
0222000000
0020001000
0000001110
0000000000
```


representation: color names
```
black black black black black red black black black black
blue blue black black red red red black black black
blue blue black black black red black black black black
black black black black black black black black blue black
black black black black black black black blue blue blue
black black red black black black black black blue black
black red red red black black black black black black
black black red black black black blue black black black
black black black black black black blue blue blue black
black black black black black black black black black black
```


representation: Excel
```
,A,B,C,D,E,F,G,H,I,J
1,0,0,0,0,0,2,0,0,0,0
2,1,1,0,0,2,2,2,0,0,0
3,1,1,0,0,0,2,0,0,0,0
4,0,0,0,0,0,0,0,0,1,0
5,0,0,0,0,0,0,0,1,1,1
6,0,0,2,0,0,0,0,0,1,0
7,0,2,2,2,0,0,0,0,0,0
8,0,0,2,0,0,0,1,0,0,0
9,0,0,0,0,0,0,1,1,1,0
10,0,0,0,0,0,0,0,0,0,0
```


representation: emoji
```
⚫⚫⚫⚫⚫🔴⚫⚫⚫⚫
🔵🔵⚫⚫🔴🔴🔴⚫⚫⚫
🔵🔵⚫⚫⚫🔴⚫⚫⚫⚫
⚫⚫⚫⚫⚫⚫⚫⚫🔵⚫
⚫⚫⚫⚫⚫⚫⚫🔵🔵🔵
⚫⚫🔴⚫⚫⚫⚫⚫🔵⚫
⚫🔴🔴🔴⚫⚫⚫⚫⚫⚫
⚫⚫🔴⚫⚫⚫🔵⚫⚫⚫
⚫⚫⚫⚫⚫⚫🔵🔵🔵⚫
⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫
```


representation: python dictionary
```python
{'width':10,'height':10,'background':0,(5,0):2,(0,1):1,(1,1):1,(4,1):2,(5,1):2,(6,1):2,(0,2):1,(1,2):1,(5,2):2,(8,3):1,(7,4):1,(8,4):1,(9,4):1,(2,5):2,(8,5):1,(1,6):2,(2,6):2,(3,6):2,(2,7):2,(6,7):1,(6,8):1,(7,8):1,(8,8):1}
```


representation: RLE
```
10 10 d02c0,a1a0b2b0,a1b02c0,g010,f0b1,a02d010,0b2e0,a02b01b0,e0b10,0
```


representation: RLE transposed
```
10 10 0a1f0,0a1b02b0,d0b2a0,e02b0,02g0,b2f0,02d0a10,c01b010,b0b1a010,c01d0
```


## Test Pair Input

- width: 10
- height: 10
- number_of_unique_colors: 2
- most popular color: (0 black ⚫)
- least popular color: (1 blue 🔵)
- color (0 black ⚫), count 73
- color (1 blue 🔵), count 27


representation: digits
```
0000000010
0000000111
0111000010
0101000000
0111000000
0000000000
0000001100
0111000000
0101000011
0111000011
```


representation: color names
```
black black black black black black black black blue black
black black black black black black black blue blue blue
black blue blue blue black black black black blue black
black blue black blue black black black black black black
black blue blue blue black black black black black black
black black black black black black black black black black
black black black black black black blue blue black black
black blue blue blue black black black black black black
black blue black blue black black black black blue blue
black blue blue blue black black black black blue blue
```


representation: Excel
```
,A,B,C,D,E,F,G,H,I,J
1,0,0,0,0,0,0,0,0,1,0
2,0,0,0,0,0,0,0,1,1,1
3,0,1,1,1,0,0,0,0,1,0
4,0,1,0,1,0,0,0,0,0,0
5,0,1,1,1,0,0,0,0,0,0
6,0,0,0,0,0,0,0,0,0,0
7,0,0,0,0,0,0,1,1,0,0
8,0,1,1,1,0,0,0,0,0,0
9,0,1,0,1,0,0,0,0,1,1
10,0,1,1,1,0,0,0,0,1,1
```


representation: emoji
```
⚫⚫⚫⚫⚫⚫⚫⚫🔵⚫
⚫⚫⚫⚫⚫⚫⚫🔵🔵🔵
⚫🔵🔵🔵⚫⚫⚫⚫🔵⚫
⚫🔵⚫🔵⚫⚫⚫⚫⚫⚫
⚫🔵🔵🔵⚫⚫⚫⚫⚫⚫
⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫
⚫⚫⚫⚫⚫⚫🔵🔵⚫⚫
⚫🔵🔵🔵⚫⚫⚫⚫⚫⚫
⚫🔵⚫🔵⚫⚫⚫⚫🔵🔵
⚫🔵🔵🔵⚫⚫⚫⚫🔵🔵
```


representation: python dictionary
```python
{'width':10,'height':10,'background':0,(8,0):1,(7,1):1,(8,1):1,(9,1):1,(1,2):1,(2,2):1,(3,2):1,(8,2):1,(1,3):1,(3,3):1,(1,4):1,(2,4):1,(3,4):1,(6,6):1,(7,6):1,(1,7):1,(2,7):1,(3,7):1,(1,8):1,(3,8):1,(8,8):1,(9,8):1,(1,9):1,(2,9):1,(3,9):1,(8,9):1,(9,9):1}
```


representation: RLE
```
10 10 g010,f0b1,0b1c010,0101e0,0b1e0,0,e0a1a0,0b1e0,0101c0a1,0b1c0a1
```


representation: RLE transposed
```
10 10 0,a0b1a0b1,a0101a0101,a0b1a0b1,0,,e01b0,01c01b0,b1d0a1,01e0a1
```


## Test Pair Output

This is what the model should predict. Before giving the answer, please reflect on what transformation happens.

My own thoughts about the output:
- I guess these colors are likely present in the output: (0 black ⚫), (1 blue 🔵), (2 red 🔴)
- The output size is the same as the input size.

# Task A - Compare the training pair 0 and pair 1

Establish reasoning steps linking inputs to their outputs.

# Task B - Apply rules to the training pair 0

Apply the hypothesized rule to the 'train 0 input' and see if it yields the 'train 0 output' image.

# Task C - Apply rules to the training pair 1

Apply the hypothesized rule to the 'train 1 input' and see if it yields the 'train 1 output' image.

# Task E - Predict the output using the generalized transformation

Use excel speadsheet representation for the output.

Rate how confident you are in your prediction.

# Task F - double check your own answer

Describe the transformation from the input to the output.
Verify that the pixels in the output are placed at the same positions that you had in mind.
After the double check, rate how confident you now are in your prediction.

# Task G
create a RLE representation of the predicted output

---

Noticing differences
I’m piecing together the differences between the input and output. Comparing pixel colors reveals replacements: some blue pixels turned red, and the black count increased.
Tracking transitions
I’m thinking about how 16 blue pixels shifted to black and red. The transitions highlight color changes and possible shape alterations in the output.
Piecing together changes
I’m examining the “digits” representation, noticing how certain blue pixels turned black or red. New pixels, including a newly introduced blue one, were introduced at specific positions.
Observing pixel shifts
I’m compiling how pixels transition: a black pixel morphs into red, and a new blue pixel appears. This intrigue brings the minimalist transformation approach into sharper focus.
Spotting patterns and shifts
I’m observing the transformation: black pixels morph into red, and new blue ones emerge. Ensuring distribution within designated coordinates confirms the changes.
Spotting shifts
Hmm, I’m thinking about the pattern: each trio of blue pixels turns red in the middle, with the outer ones switching to black. This suggests a specific transformation rule.
Noticing pattern shifts
I’m working through the puzzle, focusing on horizontal symmetrical patterns. Interestingly enough, triple blue pixels often transform into the sequence 0 2 0 in the output.
Noticing the pattern
I’m analyzing rows with triple consecutive blues. The output shifts these to 2,2,2 in red, maintaining a consistent transformation for those specific patterns.
Tracking transformation patterns
I’m noticing that triple consecutive blue pixels consistently change to 2,2,2 in red. Interestingly, the final blue triplet in any pattern remains unchanged.
Analyzing transformation patterns
I’m curious about how the initial 1,1,1 trio in each line consistently changes to 0,2,0. The final trio remains blue, even though other patterns also transition.
Tracking transformation patterns
I’m noting two main transformations: 1,1,1 turns into 0,2,0 and 1,0,1 shifts to 2,2,2. We apply these to only the first occurrence of each pattern per line.
I’m rethinking the rule
Interestingly enough, some patterns supposed to transform aren’t. Context might influence which patterns get altered, leading me to refine the transformation rules.
Noticing inconsistencies
OK, so 111 patterns in line 0 and line 2 shift to 0,2,0, but line 5’s 111 stays 111. This makes me think the rule isn’t consistent.
Analyzing transformation rules
I’m examining patterns with 111 and 1,0,1. It seems only the first occurrence of these patterns in each row gets transformed, creating some interesting patterns.
Assessing vertical patterns
I’m curious about the idea that 111 transformations happen when the triple is at the top of a shape, not below another 111 pattern. This might clarify the transformation rule.
Tracing transformation patterns
I’m mapping out why 111 shifts occur when a 1,0,1 pattern is nearby. It seems this method might clarify the transformation rule, especially in a vertical/horizontal dimension.
Examining transformations
I’m noticing that only the initial 111 pattern in each row is transformed to 0,2,0. This pattern of transformation consistently emerges when analyzing different entries.
Revisiting line5’s pattern
Interestingly enough, I’m rethinking why line5’s 111 doesn’t transform. It appears that only the initial 111 in a row converts to 0,2,0, and the final 3 stays blue.
Revisiting line5’s consistency
I’m noting that while earlier lines show the initial 111 converted to 0,2,0, the final 3 remains blue, maintaining the pattern.
Assessing transformation patterns
Considering if 111 transformations occur only when a 0 is absent between the pattern and the shape’s border. This adjustment might clarify the pattern.
Rechecking the pattern
I’m confirming the 111 transformation in the output data due to the puzzle’s constraints. Ensuring accurate input and output alignment is crucial for consistency.
Tracking transformation hints
Analyzing the second training pair, it seems 1,0,1 patterns adjust to 2,2,2. Grasping the transformation rule demands a detailed look at these changes.
Confirming patterns
Interestingly enough, for the second training pair, the transformations of 111 to 0,2,0 and 1,0,1 to 2,2,2 consistently hold. Each line manages one triple replacement.
Evaluating transformation rules
I’m thinking about handling 1,0,1 and 111 patterns line by line, replacing only the first triple per line to keep the transformation consistent.
Tracking transformation rules
I’m piecing together that 1,0,1 patterns are always transformed, while 111 patterns shift only if no similar triple exists in nearby lines. This contextual logic guides transformations.
Tracing the pattern
I’m piecing together the transformation rules: spot the first 111 or 1,0,1 in each line, then swap it with 0,2,0 or 2,2,2. Subsequent triples stay as they are.
Evaluating transformation rules
I’m examining 111 and 1,0,1 patterns, noting the initial transformations to 0,2,0 or 2,2,2. What’s clear is the first triple in each line gets affected.
Wondering about line5
It’s interesting to see that line5 doesn’t fit the pattern transformation rule, even though it has the 111 triplet. This indicates there might be a special circumstance for this line.
Tracing transformations
Mapping out how 1,0,1 and 111 patterns in line5 are handled, especially in sequences influencing the final row. The goal is to identify transformation patterns.
Testing for symmetry
By focusing on the middle line, I’m analyzing symmetry and patterns, considering the effects on the overall image’s balance and reflection. Progressing through each row methodically.
Analyzing adjacency effects
I’m considering how adjacency might be impacting transformations, especially in pair1 where 111 at line5 is replaced, but not in pair0. Adjusting for these dynamics is crucial.
Understanding row patterns
I’m considering how transformations are crafted by patterns in columns and rows. Shifts only happen with 1,0,1 patterns next to 111, orchestrating intricate shapes across lines.
Spotting trends
I’m looking at the approach: identify the leftmost pattern 111 or 1,0,1 in each row, replace it, and keep other patterns intact. Odd that line5’s 111 remains unchanged.
Examining the rules
I noticed the initial and final patterns differ in line5. It seems there are no conditions tied to flanking or adjacent colors for transformations.
Charting the course
Moving forward, 111 and 1,0,1 transformation rules are applied to the first encountered triple in each line, with line5 possibly being an anomaly or trick.
Adjusting my approach
I’m tackling 111 and 1,0,1 transformations, but line5’s role is ambiguous. It might stay unchanged or reflect symmetry in a larger pattern.
Piecing together transformation methods
I’m noting how 111 is swapped to 0,2,0 and 1,0,1 to 2,2,2 in the first row. This covers all possible patterns of interest.
Piecing together
OK, let me see. On odd lines, 1,0,1 patterns are replaced, while 111 patterns are replaced on even lines, which explains why line5 remains unchanged.
Confirming the rule
I’m concluding that for even lines, 111 changes to 0,2,0, and for odd lines, 1,0,1 changes to 2,2,2, with only the first encountered triple being transformed.
Adjusting the strategy
Noticing inconsistencies with parity rules, it seems 1,0,1 might take precedence over 111 transformations. This shift clarifies the rule for optimally reducing blue pixels.
Identifying the rule
I’ve pinpointed the transformation pattern: locate the initial 111 or 1,0,1 in each line, replace it, and maintain other patterns. Use the identified pattern to simplify the transformation process.
Confirming the alignment
I’m checking the alignment of output line5 with pair0. It seems no change was meant, based on the consistent patterns and labels. The rule for transformations looks solid now.
Confirming transformations
I’m checking the output lines to ensure 111 and 1,0,1 were correctly transformed to 0,2,0 and 2,2,2 respectively, using the identified rule.
Spotting transformations
OK, I’m piecing together how 111 and 1,0,1 transform to 0,2,0 and 2,2,2. Each line gets only one modification based on these patterns, ensuring the correct rule application.
Confirming transformations
I’m tracking each pattern shift, ensuring 111 and 1,0,1 transform to 020 and 222 in the first occurrence. Despite a minor anomaly, the pattern is generally consistent.
Mapping out RLE patterns
I’m sizing up run-length encoding for patterns: 111 changes to 020 and 1,0,1 to 222. Each line gets a concise run-length code. This method keeps things streamlined.
Crafting the RLE
I’m pulling together run-length encoding for each line’s patterns: counting zeros and colors to form concise codes. This approach ensures efficient communication.
Reworking run-length encoding
I’m re-evaluating the mapping codes for patterns in each line, ensuring accuracy with zeros and colors, aiming for clear and concise representations.
Mapping run-length patterns
I’m detailing run-length encoding for sequences like 0222000000 and 0020000011. This method ensures patterns are systematically represented, enhancing data consistency and clarity.

Step-by-step Reasoning (with confidence ratings on observations)
	•	Observing Training Pair 0 and Pair 1:
The output introduces a new color (red = 2) based on patterns of blue pixels (1). (medium)
Identified patterns:
	•	A horizontal triple of blue pixels 111 is transformed into 0,2,0. (weakly positive)
	•	A horizontal pattern of blue-black-blue 1,0,1 is transformed into 2,2,2. (weakly positive)
Only the first such pattern in each row is transformed. Subsequent patterns are left as is. (weakly positive)
Checked across train pairs: mostly consistent except one anomaly in train pair 0 line 5. Possibly just a special case or data noise. (weakly negative about anomaly explanation)
Overall rule seems stable:
If row contains 1,0,1 (B-black-B) pattern first, transform it to 222. Else if row contains 111 (triple B), transform it to 020. Stop after the first found pattern. (medium)
	•	Applying to Train Pair 0 & 1 matches the given outputs for most lines. (weakly positive)
	•	Applying to Test Pair Input:
For each row of the test input (0-based indexing):

Input -> Analysis -> Output
line0: 0000000010 no triple 111 or 1,0,1 -> unchanged -> 0000000010
line1: 0000000111 first triple = 111 at col7,8,9 -> 020 -> 0000000200
line2: 0111000010 first triple = 111 at col1,2,3 -> 020 -> 0020000010
line3: 0101000000 first triple = 1,0,1 at col1,2,3 -> 222 -> 0222000000
line4: 0111000000 first triple = 111 at col1,2,3 -> 020 -> 0020000000
line5: 0000000000 no pattern -> unchanged -> 0000000000
line6: 0000001100 only 1,1 no triple -> unchanged -> 0000001100
line7: 0111000000 first triple = 111 at col1,2,3 -> 020 -> 0020000000
line8: 0101000011 first triple = 1,0,1 at col1,2,3 -> 222 -> 0222000011
line9: 0111000011 first triple = 111 at col1,2,3 -> 020 -> 0020000011



Final Predicted Output (Excel-like) (Task E):
Indexing columns from A to J:

   A B C D E F G H I J
1: 0 0 0 0 0 0 0 0 1 0
2: 0 0 0 0 0 0 0 2 0 0
3: 0 0 2 0 0 0 0 0 1 0
4: 0 2 2 2 0 0 0 0 0 0
5: 0 0 2 0 0 0 0 0 0 0
6: 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 0 0 1 1 0 0
8: 0 0 2 0 0 0 0 0 0 0
9: 0 2 2 2 0 0 0 0 0 1 1
10:0 0 2 0 0 0 0 0 0 1 1

Confidence before double-check: weakly positive.

Double-check (Task F):
	•	The identified pattern was consistently applied to all lines.
	•	The transformations match the rule established from the training pairs.
After double-checking, confidence: medium.

RLE Representation of the Predicted Output (Task G)

Using the lines in digit form (0=black,1=blue,2=red):

Line0: 0000000010
	•	8 zeros + 1 blue + 1 zero
	•	Run lengths: 8 zeros = ‘g0’, then ‘1’, then ‘0’
RLE: g0 1 0

Line1: 0000000200
	•	7 zeros = ‘f0’, then ‘2’, then ‘00’ = ‘a0’
RLE: f0 2 a0

Line2: 0020000010
	•	‘0 0’ = ‘a0’, then ‘2’, then ‘0 0 0 0’ = ‘c0’, then ‘1’, then ‘0’
RLE: a0 2 c0 1 0

Line3: 0222000000
	•	‘0’, then ‘2 2 2’ = ‘b2’, then ‘0 0 0 0 0’ = ‘d0’ (5 zeros)
RLE: 0 b2 d0

Line4: 0020000000
	•	‘0 0’ = ‘a0’, ‘2’, ‘0 0 0 0 0 0’ = ‘e0’ (6 zeros)
RLE: a0 2 e0

Line5: 0000000000
	•	10 zeros = ‘i0’
RLE: i0

Line6: 0000001100
	•	‘0 0 0 0 0 0’ = ‘f0’ is 7 zeros? Need exactly 6 zeros: ‘e0’ = 6 zeros
	•	Then ‘1 1’ = ‘a1’ (2 ones)
	•	‘0 0’ = ‘a0’ (2 zeros)
RLE: e0 a1 a0

Line7: 0020000000 same as line4
RLE: a0 2 e0

Line8: 0222000011
	•	‘0’, ‘2 2 2’=‘b2’, ‘0 0 0 0’=‘c0’, ‘1 1’=‘a1’
RLE: 0 b2 c0 a1

Line9: 0020000011
	•	‘0 0’=‘a0’, ‘2’, ‘0 0 0 0 0’=‘d0’ (5 zeros), ‘1 1’=‘a1’
RLE: a0 2 d0 a1

Done.

Final Confidence: medium.

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Thinking for 6m16s.

Conclusion: 
Comes very close. Only 3 pixels incorrect in the top right corner.
