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• '100 Lockers' and factoring
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  One can also think of this puzzle in terms of factoring. Any number that has an even number of factors (e.g., 12's factors are 1,2,3,4,6,12) will result in a closed locker. Any number that has an odd number of factors (e.g., 25's factors are 1,5,25) will result in an open locker. Thus, only perfect squares (where two of the factors are identical) will result in open lockers.

  Posted by walaszek on February 17, 2007 at 19:52:32 Pacific Time

• Matter of Degree, part 2
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  I think the answer to the question could just as easily be 12, rather than 11. Nowhere does the question exclude the crossing at noon (or midnight). It's not as if that time doesn't exist! I think the confusion stems from using 12 as an endpoint, and if the interval is "open" or "closed" at one or both of the ends.
  
  For example, use the exact same reasoning as the answer given, but replace the "starting point" of 12 with 6 o'clock. Then, you would simply say "for each hour the minute hand clearly passes the hour hand, and there are 12 hours on the clock, so by the time the hour hand returns to 6 there have been 12 crossings".

  Posted by oberman77 on March 09, 2007 at 05:23:26 Pacific Time

• Matter of Degree, part 2
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  Well, I was wrong. I'm glad I thought about this one. I was worried about the edge case in the given answer caused by starting/ending at 12. By starting at 6 o'clock, I thought it would clear up any subtle issues. It does, and the answer really is 11. I thought each hour would get it's own passing, but the 11th hour has no crossing (or 11 and 12 share depending on how you think about it). Ooops.

  Posted by oberman77 on March 09, 2007 at 06:48:24 Pacific Time