Question

How many different positive integers can be represented as a difference of two distinct members of the set {1, 2, 3, 4, 5, 6}?

Answer 1

For the difference to be positive, when both the minuend and the subtrahend are positive, the former must be greater than the latter.

Therefore

minuend = 2 ⇒ subtrahend = 1 ← 1 number

minuend = 3 ⇒ subtrahend = 1,2 ← 2 numbers

minuend = 4 ⇒ subtrahend = 1,2,3 ← 3 numbers

minuend = 5 ⇒ subtrahend = 1,2,3,4 ← 4 numbers

minuend = 6 ⇒ subtrahend = 1,2,3,4,5 ← 5 numbers

1+2+3+4+5=15

Answer 2

5

Explanation:

6 - 1 = 5, 5 - 1 = 4, all the way down to 2 - 1 = 1.

This is the set {1, 2, 3, 4, 5}, which is a list of 5 values. lol