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.
