Problem 23 · 2010 Math Kangaroo
Stretch
Logic & Word Problems
careful-countingcasework
In the grid, how many grey squares have to be coloured white so that each row and each column contains exactly one grey square?
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Answer: C — 6
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Hint 1 of 2
When you are done there can be only one grey square in each of the 5 rows, so exactly 5 grey squares survive.
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Hint 2 of 2
Count all the grey squares now, then take away the 5 you get to keep.
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Approach: count the grey squares, keep just 5
- The finished grid keeps exactly one grey square per row and per column, which is 5 grey squares in all.
- Counting the picture, there are 11 grey squares now, and you can pick 5 of them with one in every row and column.
- So you must colour \(11 - 5 = 6\) grey squares white — the answer is C.
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