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100 doors in a Row - solution incomplete?

Isnt the the 100 doors in a row solution missing a case?

Prime Numbers have only 2 factors - The number itself and 1. For example: 7 has only 2 factors 1, 7. If all the doors are closed at start, then prime number doors will remain closed at the end as well.

Please let me know if this is a valid case.

Thanks!

Shekar
Wednesday, December 10, 2003

That case is essentially covered - that door has an even number of unique divisors - just like the 42nd door in the example (1, 2, 3, 6, 7, 14, 21, 42) - thus it is closed.

Only doors with an odd number of unique divisors will remain open (that being those which are square numbers and thus repeat a divisor).

Lou
Friday, December 12, 2003

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