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%.
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