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Problem of the Week 943

Alice and Bob, revisited

Alice chooses 100 distinct real numbers, places them in order so that a1 < a2 < ... < a100, and tells Bob their sum, the sum of their squares, and all the 98 differences a3 - a1, a4 - a2, ..., a100 - a98. Can Bob always determine the numbers?

Source: Dirk Laurie, Stellenbosch Univ., South Africa (and thanks to him for these two original problems, which I think are quite nice!)
© Copyright 2001 Stan Wagon. Reproduced with permission.

9 October 2001