Devon McCormick wrote: > 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.
SPOILER AHEAD This was discussed in the forum a while ago. A solution was posted at http://www.jsoftware.com/pipermail/programming/2006-May/002352.html Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
