http://mags.acm.org/communications/200902/?pg=106
The first one: Five integers with a positive sum are assigned to the vertices of a pentagon. At any point you may select a negative entry (say, -x) and flip it to make it positive, or x, but then you must subtract x from each of the two neighboring values; thsu, the sum of the five integers remains the same. For example, if the numbers are 2, 4, -3, 1, -3, you can either flip the first -3 to get 2, 1, 3, -2, -3 or the second to get -1, 4, -3, -2, 3. Now prove that no matter what numbers you start with and strategy you follow, all the numbers will eventually become non-negative, and thus the procedure terminates after finitely many steps. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
