4x4 grid with no trominoes containing repeating colors

Question

Paint the cells of a 4x4 grid with ? colors, such that every possible tromino found in the grid uses 3 different colors. What is the smallest value of ? possible in such a coloring?

Bubbler · Accepted Answer

I think we need at least

with the example coloring of

To see this is the minimum, first consider

Then, consider one of the colors used to color a center cell:

Therefore, we conclude that

RobPratt · Answer

The minimum is

Beastly Gerbil · Answer

The smallest $n$ will be

And here’s the grid (all possible grids will be mirrors and rotations of this):

This is because

Now to find the grid

4x4 grid with no trominoes containing repeating colors

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