Staircase Climber: A Recursion Puzzle

MediumLogic PuzzlesDynamic Programming

A classic puzzle about finding the number of ways to climb stairs, which introduces the concept of recursion and the Fibonacci sequence.

The challenge

If there are 10 steps on a staircase, and you can climb either 1 or 2 steps at a time, how many different ways are there to reach the top?