18

Part of 2016 Math Prize for Girls Problems

Problems(1)

Math Prize 2016 Problem 18

Source:

T = \{ 1, 2, 3, \dots, 14, 15 \}

. Say that a subset

S

T

is handy if the sum of all the elements of

S

is a multiple of

5

. For example, the empty set is handy (because its sum is 0) and

T

itself is handy (because its sum is 120). Compute the number of handy subsets of

T

Math Prize for Girls