Question 12
The beavers have devised an interesting way to encode the letters I, T, O, C and L using a $3\times3$ numerical grid. First they draw the letters on $3\times3$ square grids as follows:
Text transcription of the letter pictures: 0 = white cell, 1 = gray cell; rows run top to bottom and columns left to right.
I
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 0 | 1 | 0 |
| 2 | 0 | 1 | 0 |
| 3 | 0 | 1 | 0 |
T
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 0 | 1 | 0 |
| 3 | 0 | 1 | 0 |
O
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 1 |
C
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |
L
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 0 | 0 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |
To encode a letter, they inspect each cell in its picture and enter the number of cells at the same position with the same color in the pictures of the other 4 letters.
For example, I is encoded by the left-hand grid below.
Left numerical grid (the example for I):
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 0 | 3 | 1 |
| 2 | 1 | 1 | 3 |
| 3 | 1 | 4 | 1 |
Right numerical grid to identify:
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 3 | 3 | 2 |
| 2 | 2 | 2 | 0 |
| 3 | 2 | 4 | 2 |
Which letter produces the right-hand numerical grid?
Text transcription of the letter pictures: 0 = white cell, 1 = gray cell; rows run top to bottom and columns left to right.
I
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 0 | 1 | 0 |
| 2 | 0 | 1 | 0 |
| 3 | 0 | 1 | 0 |
T
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 0 | 1 | 0 |
| 3 | 0 | 1 | 0 |
O
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 1 |
C
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 1 | 1 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |
L
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 1 | 0 | 0 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |
To encode a letter, they inspect each cell in its picture and enter the number of cells at the same position with the same color in the pictures of the other 4 letters.
For example, I is encoded by the left-hand grid below.
Left numerical grid (the example for I):
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 0 | 3 | 1 |
| 2 | 1 | 1 | 3 |
| 3 | 1 | 4 | 1 |
Right numerical grid to identify:
| Row / Column | 1 | 2 | 3 |
| --- | --- | --- | --- |
| 1 | 3 | 3 | 2 |
| 2 | 2 | 2 | 0 |
| 3 | 2 | 4 | 2 |
Which letter produces the right-hand numerical grid?