Choose the number which is different from others in the group.

Concept: In this style of "odd one out" puzzle, most of the given numbers satisfy one common algebraic identity — here, being exactly one more than a perfect square, i.e. n2 + 1 — while a single value is built to look similar but actually fits the mirror identity, n2 - 1. The task is to test every value against the shared identity and find the one that breaks it.

Application — testing each value:

1. 50 = 49 + 1 = 72 + 1 → fits n2 + 1 with n = 7.

2. 82 = 81 + 1 = 92 + 1 → fits n2 + 1 with n = 9.

3. 170 = 169 + 1 = 132 + 1 → fits n2 + 1 with n = 13.

4. 48 = 49 - 1 = 72 - 1 → this is one LESS than a perfect square, not one more, so it does not fit the identity the other three share.

Cross-check: If 48 were still to fit n2 + 1, then 48 - 1 = 47 would need to be a perfect square. It is not (62 = 36 and 72 = 49, with nothing in between), which independently confirms 48 genuinely breaks the shared rule.

Result: 48 is the number that is different from the rest of the group.