Ken's POTW

Bob's House, and Productive Numbers Revisited
  1. Bob lives on a long street and has noticed that the sum of the house numbers up to his own house, but excluding it, equals the sum of the numbers of his house to the end of the road. If the houses are numbered consecutively, starting from 1, what is the number of Bob's house? Assume there are less than 1000 houses on the road.

  2. Find all numbers i, such that i is equal to the sum of the cubes of its digits.

Source: 1. The Penguin Book of Curious and Interesting Puzzles, David Wells, 1992. 2. Internet newsgroup rec.puzzles.

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