Problem 7 · 2012 Math Kangaroo
Easy
Geometry & Measurement
grid-countingcareful-counting
A wall was tiled alternately with grey and striped tiles. Some tiles have fallen from the wall. How many grey tiles have fallen off?
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Answer: C — 7
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Hint 1 of 2
The wall is a checkerboard, so each missing square was either grey or striped.
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Hint 2 of 2
Find every empty square and decide its colour from the alternating pattern.
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Approach: use the checkerboard pattern to colour each gap
- The tiles alternate grey/striped like a chessboard, so a square's colour is fixed by its position.
- There are 13 empty squares in the hole.
- Working through the checkerboard, 7 of the gaps sit on grey positions and 6 on striped positions.
- So 7 grey tiles fell off.
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