Question 118643
looking at a few lockers will reveal the pattern...
___ c is closed, o is open


L1 ___ o-1
L2 ___ o-1, c-2
L3 ___ o-1, c-3
L4 ___ o-1, c-2, o-4
L5 ___ o-1, c-5
L6 ___ o-1, c-2, o-3, c-6
L7 ___ o-1, c-7
L8 ___ o-1, c-2, o-4, c-8
L9 ___ o-1, c-3, o-9
L10 ___ o-1, c-2, o-5, c-10


look at the OPEN lockers ___ 1, 4, 9 ___ see a pattern? ___ WHY?


factors for numbers occur in pairs, like for 12 __ 1,12 __ 2,6 __ 3,4
___ the first factor opens and the second closes, so the locker ends up closed


but for perfect squares, one of the pairs is the same number
___ for 36 __ 1,36 __ 2,18 __ 3,12 __ 4,9 __ 6,6
___ so there is no close to go with the open