Math CentralQuandaries & Queries


Question from lupita, a student:

Fifty houses are on the north side of a river. The 2nd house has gray siding, and every 5th house after that also has gray siding. The 11th house has a stone chimney; every 3rd house after that also has a stone chimney. How many of the 50 houses have stone chimneys but do not have gray siding?


I can help get you started.

The houses with the gray siding are houses numbered 2, 7, 12, 17 and so on.

The houses with the stone chimneys are houses numbered 11, 14, 17 and so on.

Notice that house number 17 has gray siding and a stone chimney. From then on every 5th house has gray siding end every 3rd house has a gray chimney. Since $3 \times 5 = 15$ every 15th house will have both.


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