Fill It Up
How many ways are there to fill up the rest of the square grid with purple, pink and blue squares, such that each row and each column contains exactly 1 square of each color?
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1 solution
Moderator note:
Great! Like in Sudoku, we want to find the square whose row/column has many different colors, which allows us to eliminate them accordingly.
Consider the middle row. The right square cannot be blue (because then the rightmost column has two blue squares). Since the middle row must contain a blue square, it must be that the middle square is blue. Thus, the right square in the middle row must be purple to complete it.
Likewise, consider the bottom row. The middle square cannot be pink, so the bottom-right square must be pink instead. So the middle square in the bottom row is purple.
This completes the grid, and it can be verified that it works, so there is 1 such way.