FILE No.178Unsolved
You climb a 10-step staircase one step at a time or two steps at a time. Even for the same number of steps, a different order of 1-steps and 2-steps counts as a different way.
How many ways are there to climb the 10 steps?
If you get stuck, open the hints one at a time, in order.
Split by whether the last move is 1 step or 2 steps.
Actually count the cases of 1, 2, and 3 steps.
What happens if you keep adding the previous two?
How many ways are there to climb the 10 steps?
Choose the answer closest to the truth.
89 ways
The answer is "89 ways."
The number of ways to climb n steps = (ways to climb n−1 steps) + (ways to climb n−2 steps). 1 step: 1 way; 2 steps: 2 ways; 3 steps: 3 ways; 4 steps: 5 ways, and so on, reaching 89 ways for 10 steps.
55 ways is the value for 9 steps, and 144 ways for 11 steps.
Because you try to count the 10-step case right away.
The cases on this site are fictional puzzles created for entertainment. Any resemblance to real people, organizations or events is coincidental.
© Unsolved Files
