Problem:
The diagram represents a -foot-by--foot floor that is tiled with -square-foot black tiles and white tiles. Notice that the corners have white tiles. If a -footby--foot floor is to be tiled in the same manner, how many white tiles will be needed?
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Answer Choices:
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Solution:
To maintain the pattern, white squares will always occupy the corners, and every edge of the square pattern will have an odd number of tiles. Create a table, starting with a white square in the corner of the pattern, and increase the sides by tiles.
Following the pattern, an area has squares, a area has , and a has .
There will be rows that each contain white tiles, so the total is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions