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2015-09-11T17:40:54+08:00

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Since there are 120 lockers that would mean that the locker number has 3 digits (including 0 as the first digit). Since all the digits are odd numbers we let the first digit be 2a - 1, the second be 2b - 1 and the third be 2c - 1.

(2a - 1) + (2b - 1) + (2c - 1) = 11
2(a+b+c) - 3 = 11
2(a+b+c) = 14
a + b + c = 7

We need to take note that the first digit can only be 0 or 1. Since all digits are odd a is 1.

1 + b + c = 7
b + c = 6

The possible pairs are (1,5), (2,4), (3,3), (4,2), and  (5,1). Since all digits are odd we only take the pairs (1.5), (3,3) and (5,1). The only possible locker numbers are from 100 to 120 since our first digit is 1. So we can only take the pair (1,5).

Therefore the locker number is 115. 
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