Problem:
A block wall feet long and feet high will be constructed using blocks that are foot high and either feet long or foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
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Answer Choices:
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E.
Solution:
If the vertical joins were not staggered, the wall could be build with of the two-foot blocks. To stagger the joins, we need only to replace, in every other row, one of the longer blocks by two shorter ones, placing one at each end. To minimize the number of blocks this should be done in rows , and . This adds blocks to the , making a total of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions