Fill Them Up
Probability
Level
3
How many ways are there to fill up the rest of the square grid with purple, pink, blue and yellow squares, such that each row and each column contains exactly 1 square of each color?
1
2
4
8
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1 solution
Case 1: When A is painted of purple, the color D , G and B , C are defined. Then E could be painted of purple or pink. After painting E the rest of squares in the gird are defined. So if A is purple are 2 ways of painting the grid.
Case 2: When A is painted of yellow, the color D , G and B , C are defined. Then E only could be painted of yellow. After painting E the rest of squares in the gird are defined. So if A is yellow are 1 way of painting the grid.
Case 3: When A is blue, it is alike case 2, so there is 1 way of painting the grid.
There are 4 ways to paint the grid