Colourfill

Probability Level pending

John colours each square in an empty 3 by 3 grid either red or green. Find the number of colourings such that no row or column contains more than one green square.


The answer is 34.

Satyabrata Dash by Satyabrata Dash , 20, India

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1 solution

X X
May 30, 2018

Total 0 green square, 1 1 possibility.

Total 1 green square, 9 9 possibilities.

Total 2 green squares, 9 × 4 2 = 18 \frac{9\times4}2=18 possibilities.

Total 3 green squares, 9 × 4 × 1 6 = 6 \frac{9\times4\times1}6=6 possibilities.

1 + 9 + 18 + 6 = 34 1+9+18+6=34

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