Problem 3 · 2014 Math Kangaroo
Easy
Counting & Probability
careful-countingcomplementary-counting
There are more grey squares than white. How many more?
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Answer: D — 9
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Hint 1 of 3
The picture is a 5-by-5 board, so there are 25 little squares in all.
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Hint 2 of 3
The white squares are easy to count because they sit together in the middle — count those first.
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Hint 3 of 3
Once you know how many are white, the rest are grey, and you compare the two piles.
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Approach: count the few white squares, then the grey ones are all the rest
- The big square is 5 across and 5 down, so it has 25 small squares altogether.
- Count the white squares in the middle: 3 on top, 2 in the middle row, 3 on the bottom, which is 8 white.
- The grey squares are all the others: 25 − 8 = 17 grey.
- Grey has 17 and white has 8, so there are 17 − 8 = 9 more grey squares.
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