# Simple grid deduction puzzle

I will let you figure the rules of this one yourselves.

Here is the empty grid to assist solvers.

Here is a text version of the grid:

 _______________________________________________________________________________________________________________
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       |       | C G P |       | C G W |       |       |       |       |       |       |       |       |       |
| C G P |  C G  |       |  G Y  |       | C G P | C G Y | G P Y | G P Y |  G Y  | G P Y | G O Y |  G O  | G O Y |
|       |       |  W Y  |       |   Y   |       |       |       |       |       |       |       |       |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       |       | C G P |       | C G W |       | C G O |       | G O P |       | G P R | C G O |       | C G O |
| C G P | G P R |       | G R W |       | G P W |       | G O P |       | G P R |       |       | C G Y |       |
|       |       | R W Y |       |   Y   |       | P W Y |       |  R Y  |       |   Y   |   Y   |       |   Y   |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       | C G O | C G O | G O R | C G W |       | C G O |       | G O R |       | B G R | B C G |       |       |
|  C G  |       |       |       |       | C G R |       | G R Y |       | B G Y |       |       | G O W | C G O |
|       |   R   |   Y   |   Y   |   Y   |       | R W Y |       |   Y   |       |  W Y  |  O W  |       |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|   G   | G O R |  G R  | G O R |  G W  | G R W | G O W | G O R | G O R | B G R | G R W | B C G | C G W |  C G  |
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       |       |       |       |       |       |       |       |       |       | B C G | B C G | B C G |       |
| G O W | G O W | G O W |  G O  |  B G  | B G R | B G R |  G R  |  G W  | B G W |       |       |       |  B G  |
|       |       |       |       |       |       |       |       |       |       |   W   |   W   |   W   |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       | G O P |       |       |       |       |       |       |       |       | C G P |       | B C G |       |
| G R W |       | G P W | G O P | B G O | C G O | B C G | B C G | B G W |  B G  |       | G P W |       |  G W  |
|       |   R   |       |       |       |       |       |       |       |       |   W   |       |  P W  |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
| C G O | C G O |       | G O P |       | B C G |       | B C G |       | B G W | C G O | C G O | B C G | B G R |
|       |       | C G W |       | B G W |       | B G R |       | G W Y |       |       |       |       |       |
|  W Y  |P R W Y|       |   W   |       | O R W |       |  R Y  |       |   Y   |  P W  |  R W  | O P R |   W   |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
| B C G | B G P | C G P | G O P |       | C G O |       | B C G |       | B G R | G O P | G P R | C G O | C G R |
|       |       |       |       | G O P |       | C G P |       | B G R |       |       |       |       |       |
|   R   |  R Y  |   Y   |  W Y  |       | P R W |       |  R Y  |       |   Y   |  R Y  |  W Y  | P W Y |   W   |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|
|       |       |       |       |       |       |       |       |       |       |       |       |       |       |
|       | B C G |       |       |       |       |       |       |       |       | G O R |       | C G O |       |
| C G Y |       |  C G  | G W Y | G P W | G R W | G P R | G R Y | G R Y |  G Y  |       | G O R |       |  G R  |
|       |   Y   |       |       |       |       |       |       |       |       |   Y   |       |  R Y  |       |
|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|_______|

• ^vote before even thinking, just for laying out the grid in 3, count 'em, three, formats. (4, even, including the blank.) – humn Jan 14 '17 at 20:34
• @humn, well, I got help with that. :) Rubio helped with one of the formats. – Maria Deleva Jan 14 '17 at 20:35

This is more of a continuation of rand al'thor's answer.

As Rand al'thor surmised the letters indicate that that cell has a cell with the corresponding colour as one of its neighbours. For instance the cells which include a Y are:

From which we can readily deduce the yellow cells are just the ones indicated. We repeat for B(rown), O(range), C(yan), R(ed), P(urple), W(hite).

Now every cell has a 'G' (which might be an error, since for all the other cases a cell doesn't include its own colour indicator) so we can skip that since it only tells us all the remaining cells are green (I have used gray though).

You end up with the following (but here mapping G to gray, rather than green).

Spelling out the message "YOU ROCK".

• Note for the text version of the grid we need to change the bottom element of the second column to B C G Y to match the image.
• Well, I would have got this, if there hadn't kept being mistakes in the question :-/ – Rand al'Thor Jan 16 '17 at 0:33
• Only it is BCGY. Am I misunderstanding you? @rand I apologize for all the mistakes, if I could downvote my own question, I would. But I fixed them yesterday. – Maria Deleva Jan 16 '17 at 6:54
• @MariaDeleva Ah it's only BCGR in the text version. – Neil W Jan 16 '17 at 7:13
• Can we have a working explanation? – boboquack Jan 16 '17 at 7:15
• @MariaDeleva +NeilW - text grid is fixed now – Rubio Jan 16 '17 at 9:08

## The rule

The letters refer to colours: BCGOPRWY denoting Brown, Cyan, Green, Orange, Purple, Red, White, Yellow respectively. These colours can be seen by clicking on the grid in the OP to reveal a colour palette.

The set of letters in each cell refers to the set of colours that cell can 'see', i.e. the colours a chess king on that cell could move onto in a single move. (Diagonal must count as well as orthogonal, because some cells have as many as seven letters. The cell's own colour doesn't count, because that would swiftly lead to contradictions.)

## The solution (work in progress)

Let us denote the columns by a-n and the rows by 1-9.

NOTE: the question contains an error. (There should be a W next to d5. But it can't be on row 4 because of d3, nor in column c because of b5, nor at e5, e6, or d6 because of each other.) This answer is on hold until the question has been fixed and checked.

1. The obvious place to start is a4, that lone G on the left-hand side: all cells around it must be green. a4 itself is next to a3, so must be cyan or green, but it can't be cyan as it's next to a5 too, so we have a big green block around a4.

2. Everything next to a3 must be green or cyan, and we can deduce which is which by looking at the letters surrounding them (a2 can't be cyan because of b2, so b2 is cyan and a2 is green). Everything next to c4 must be green or red, and again we can deduce which is which in most cases. The only possibility for a1 (next to both b1 and b2) is green, and ditto for c1 and c2 (next to both b1 and d1). Now a2 must be next to a purple, so b1 is purple; and b3 must be next to an orange, so c4 is orange. So far we have:

(I've used a red letter to denote the colour which actually fills each cell. Filling the cells with colour at this stage would look ugly and make the black letters harder to read.)

3. c1 still needs to be next to white and yellow, so d2 is yellow and d1 is white. Everything next to e5 must be blue or green, and we can swiftly deduce which is which; ditto with e4 and green or white. e1 and e2 are next to both d1 and f1, so they must be green. Now e3 must be next to a cyan, so f2 is cyan. f1 is next to both f2 and g1, so it must be green. Meanwhile, a5 still needs to be next to orange and white, so they must be a6 and b6 respectively. c6, being next to both c7 and d6, must be green. So far we have:

4. a6 must be next to a red, so a7 is red. b7 is next to a6 and c8, so it must be green. c6 is next to a purple, so c7 is purple. d6 is next to an orange, so e7 is orange. d7 and d8 are next to e7 and e8, so they must be green. So far we have:

• And what of the Os near the top left which see none? Am I missing something in this answer? – Will Jan 14 '17 at 19:42
• @Will No, Maria is missing something in the question (i.e. there's a mistake in the OP). I've let her know in chat and I'm waiting on her to fix it and triple-check everything. – Rand al'Thor Jan 14 '17 at 22:06
• I think the only thing that needs to change is the bottom element of the second row should be B C G Y. – Neil W Jan 16 '17 at 0:24