Ponder This — March’s Challenge!

Are you a professional problem solver? If so, we invite you to submit your “Ponder This” solution for this month’s challenge. Ponder This is IBM Research’s monthly brain-twister where you can match wits with some of the best minds at IBM.

Ponder This Challenge:

N lamps are set in a circle, and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps.
Find a possible N which satisfies the following statements:

  • The sum of its digits is less than 10.
  • By applying the tool for M=105 several times, we can toggle a single lamp.
  • If we remove one lamp and start from a random initial setting for the remaining N-1 lamps, the probability that there exists a way to apply the tool for M=32 several times and switch all the lamps off is less than 0.001%.

__________

IBM Research will post the names of those who submit a correct, original solution to their website! If you don’t want your name posted then please include such a statement in your submission. Send your submission to the webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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