Problem 1160 was solved by Richard Boardman, Joseph DeVincentis, Mark Krusemeyer, and Ken Duisenberg.
Boardman's proof that 4 is optimal is nice and short:
For any 4 numbers, no more than 4 of the 6 possible pair sums can be
factors. Let the 4 numbers be a, b, c, d in ascending order. Then c + d
and b + d must exceed half the total and cannot be factors.
There are many sets of 4 numbers with 4 pairs as factors, e.g., 1, 5, 7, 11.
[Back to Problem 1160]
© Copyright 2012 Stan Wagon. Reproduced with permission.