# Nontechnical Proof of “Puzzle on coins: Designing an operation”

A square table has a coin at each corner. Design an execution sequence, each of whose steps consists of one of the following operations:

ONE (O): The operation (randomly) chooses a coin and flips it. SIDE (S): The operation (randomly) chooses a side of the table and flips the two coins along that side. DIAG (D): The operation (randomly) chooses a diagonal of the table and flips the two coins along that diagonal.

such that at some point during the execution (not necessarily at the end), a state where all coins are turned the same way (all heads or all tails) obtains.

The desired answer is O, D, S, D, O, D, S, D.

Is there a non-technical proof of this answer, and how one may arrive at it?

• What would you consider to be a "non-technical proof"? Apr 29 '15 at 11:10
• An answer that a curious (curious enough to try this puzzle) would have a fair chance to understand. Apr 29 '15 at 11:36
• Have you seen kedargodbole.blogspot.com.au/2008/07/… ? Apr 29 '15 at 11:40
• I did. It may be my incompetence, but I don't see it self-evident as a proof. Apr 29 '15 at 11:50
• A variation of the problem is discussed, and some references given, at gurmeet.net/puzzles/tumblers-on-a-rotating-table Apr 29 '15 at 11:59