Paint Color Logic Puzzle

This is a walkthrough for my Paint Color Logic Puzzle over on Sporcle.

Some important things to notice beforehand:

• • Primary colors are red, yellow, and blue; secondary colors (i.e. a mix of two primaries) are orange, green, and purple.

  • Mixing equal colors gives the same color: if you mix red paint with red paint, you still have red paint.

  • 'Between' includes diagonals: this means that for 'between', a cell can be 'between' two others in any direction. For example: B2 is 'directly between' B1 & B3 (vertically), A2 & C2 (horizontally), A1 & C3 (diagonally) and A3 & C1 (diagonally).

1. You start with this grid, with A1 (red) and C3 (yellow) given.

2. A1's clue tells you that B2, which is directly inbetween two cells with primary colors (A1 and C3) has to be the mix of those. Red + yellow = ORANGE.

3. B2's clue tells you that C1 has a primary color. That means that B1 and C2 are directly between primary colors and have to contain the secondary color from mixing A1 & C1 (for B1) or C1 & C3 (for C2). If C1 were red, that would mean that B1 is also red, but that is impossible due to C3's clue (no color is adjacent to itself). Same goes for C1 being yellow, with respect to C2. The only primary color left is BLUE.

4. With C1 being blue, you can tell the colors in B1 and C2: they are simply mixes. For B1, red + blue = PURPLE; for C2, blue + yellow = GREEN.

5. C2's clue tells you that E3 is primary. It can't be yellow, because then D3 would be yellow, creating an adjacency. It can't be blue, because then D3 would be green, which would create an adjacency with C2. This means E3 is RED.

Now, you can fill D2 and D3 with the resulting mix colors (D2: blue + red = PURPLE; D3: yellow + red = ORANGE).

6. D3's clue tells you that B4 is GREEN.

7. Let's look at A3. If it were a primary color, B2 would be directly inbetween primary colors (A3 & C1), which means that it would have to be the mix of blue and the color in A3. But we know that B2 is orange, and no primary color mixed with blue results in orange. So A3 has to be a secondary color. It is already adjacent to orange (B2) and green (B4), so A3 has to be PURPLE.

8. A3's clue tells you that column D has exactly two purple cells. D2 is one. That means that D1 can't be the other one (adjacent), so either D4 or D5 has to be purple. Because of adjacency, that means that no cell that is adjacent to both D4 and D5 (i.e. C4, C5, E4 and E5) can be purple.

For C5, this means that it can't be purple, green (adjacent to B4), yellow (would create adjacency in C4 because of C3), red (would create adjacency in D4 because of E3), or blue (would create adjacency in C4 because of C3). This means that the only possibility left for C5 is ORANGE.

9. C4 is already adjacent to yellow, green, and orange, and it is going to be adjacent to the purple in D4 or D5. So C4 has to be either blue or red, i.e. a primary color. Therefore, if A2 has a primary color as well, B3 would be a secondary color (inbetween A2 & C4). But because B3 is adjacent to orange, purple, and green, it cannot contain a secondary color. That means that A2 cannot contain a primary color. As A2 is already adjacent to orange and purple, the only possibility left for A2 is GREEN.

10. Using the same logic as for A2, we can deduce that D5 cannot contain a primary color either. Because it is adjacent to orange, D5 has to be either purple or green. From D2's clue, we know that D4 is also a secondary color and it can't be orange because of adjacency, so it has to be either purple or green as well. This means that for D4 and D5, one has to be green and the other has to be purple.

Now look at E5. It cannot be purple or green (because it is adjacent to both D4 and D5), yellow (would create an adjacency in D4 because of C3), or red (would create an adjacency in E4 because of E3). So it has to be either blue or orange. If it were blue (a primary color), E4 would be purple because E3 is a primary color as well. But we know that either D4 or D5 is going to be purple, so E4 cannot be purple, which in turn means that E5 cannot be blue. This leaves ORANGE as only possibility for E5.

11. D4 has to be directly inbetween two primary colors. Because C5, D3, and E5 all contain secondary colors, D4 can only be inbetween primary colors if those primary colors are in C4 and E4.

Because E4 has to be a primary color, if E2 would contain a primary color, that would mean that E3 had to be secondary. But E3 is red, i.e. primary, so E2 cannot contain a primary color and is secondary. E2 is already adjacent to purple and orange, so it has to be GREEN.

12. Using the same logic that we've applied a couple of times already, we can deduct E1. Because C1 is blue, C3 is yellow and E3 is red, if E1 were primary, you would create an adjacency in either D1, D2 or E2. So E1 has to be secondary, and because it is adjacent to purple and green, it has to be ORANGE.

13. Because D1 is adjacent to all three secondary colors, it has to be primary. We already knew that B3 is going to be either red or blue (so primary as well). C2 is directly inbetween D1 and B3, so it has to be the mix of the colors in D1 and B3, which have to be blue and yellow (in any order) to create green. Because D1 is adjacent to blue and B3 is adjacent to yellow, D1 has to be YELLOW and B3 has to be BLUE.

14. We know from before that C4 has to be either blue or red (step 9). Because C4 is now adjacent to blue, we know that it has to be RED.

15. D4 has to be either green or purple (step 10) and it has to be the mix of C4 and E4 (step 11). No primary color, when mixed with red (C4) gives green, so D4 has to be PURPLE. This means that the primary color in E4 has to be BLUE.

16. Now we know that D4 is purple, we also know that D5 is GREEN (remember step 10).

17. Because of adjacency, A4 has to be either yellow, red, or orange. If A4 contains a primary color, B4 would be between two primary colors in A4 and C4, and would have to contain the mix of those colors. We know that B4 is green and C4 is red. No primary color can mix with red and give green as a result. This means that A4 has to be a secondary color, and the only one possible is ORANGE.

18. Time to look at all secondary colored cells in the quiz and their adjacent cells that contain a primary color used to create that secondary color. B1's purple is adjacent to both red and blue. E1's orange is adjacent to yellow. A2's green is adjacent to blue. B2's orange is adjacent to yellow. Et cetera.

You will see that at this point, A4 and E5 are the only cells with secondary colors that are not adjacent to any of the primary colors used to create that secondary color. There can only be exactly one such cell in the quiz (A4's clue), and for E5, there is nothing we can do about it. So E5 is that one cell, which means that A4 will have to be adjacent to either red, yellow, or both.

Because C3 is yellow, if A5 is red or yellow, B4 would have to be orange or yellow, but B4 is not: it is green. Therefore A5 cannot be red or yellow. This means that B5 has to be either red or yellow, and because it is adjacent to red (C4), B5 has to be YELLOW.

19. A5 cannot be red or yellow (step 18), and neither can it be green or orange (adjacent). So it has to be either blue or purple. If it were purple, it would not be adjacent to any of the primary colors used to mix it. Together with E5, this would create two cells for which this is the case, thus violating A4's rule. So the only possibility left for A5 is BLUE.