## Number of the house

*February 12, 2009 at 7:32 am* *narinderberi* *
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A long street in Europe has the houses with all the odd numbers on one side and the houses with all the even numbers on the other side, as typically done in many countries throughout the world. (a) If a man lives in an odd-numbered house such that the sum of the odd numbers of all the houses on one side of his house is equal to the sum of the odd numbers of all the houses on the other side of his house, find the total number of odd-numbered houses on his street and the number of his house. Assume that the man’s house number is greater than 25 and less than 51. (b) Repeat the same problem for even numbered houses. In this case, assume that the man’s house number is greater than 50 and less than 100.

Entry filed under: Puzzles.

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