Problem 12 · 2018 Math Kangaroo
Medium
Arithmetic & Operations
divisioncareful-counting
A rectangle is split into 40 equally big squares. The rectangle has more than one row of squares. Andreas colours in all the squares of the middle row. How many squares did he not colour in?
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Answer: C — 32
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Hint 1 of 2
There must be a single middle row, so the number of rows is odd.
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Hint 2 of 2
Find odd factors of 40 to get the rows, then the columns give the size of the middle row.
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Approach: factor 40 into odd rows times columns
- A single middle row needs an odd number of rows; the only odd factor of 40 (with more than one row) is 5, so the grid is 5 rows by 8 columns.
- The middle row has 8 squares, so the uncoloured squares number 40 − 8 = 32.
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