Mitchell gill
10/2/09
The locker problem
The order of the lockers is, open, closed, closed, open, closed, closed, closed, closed, open, closed, closed, closed, closed, closed, closed, open, the pattern of closed lockers goes on and on, adding two closed lockers for every open locker. Open lockers are perfect squares, because they have an odd # of factors. Closed lockers have an even # of factors. Factors = 1, 2, 4, 8, 16 are factors for locker 16, that’s an odd # of factors.
Factors = 1, 2, 3, 6, 9, 18 are factors for 18, that’s an even # of factors. This leads up to 31 lockers being open and 961 being closed.
| Locker 1 Open odd | Locker 2 Closed even | Locker 3 Closed even | Locker 4 Open odd | Locker 5 Closed even |
| Locker 6 Closed even | Locker 7 Closed even | Locker 8 Closed even | Locker 9 Open odd | Locker 10 Closed even |
Odd = odd # of factors even = even # of factors
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