2009 AMC 8 Problems/Problem 18
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 -foot-by--foot floor is to be tiled in the same manner, how many white tiles will be needed?
Solution
In a -foot-by--foot floor, there is white tile. In a -by-, there are . Continuing on, you can deduce the positive odd integer floor has white tiles. is the odd integer, so there are white tiles.
Solution 2
After testing a couple of cases, we find that the number of white squares is , where s is the side length of the square and is rounded up to the next whole number. Therefore, rounded up is 8, so , or .
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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