Problem 4 · 2010 Math Kangaroo
Easy
Logic & Word Problems
off-by-one
A staircase has 21 steps. Nick and Mike count the steps, one from bottom to top and the other from top to bottom. They meet at one step, which Nick counts as the 10th. Which number does Mike give this same step?
Show answer
Answer: C — the 11th
Show hints
Hint 1 of 2
They both count the very same step, just starting from opposite ends.
Still stuck? Show hint 2 →
Hint 2 of 2
On a 21-step staircase, think about how many steps sit below the meeting step and how many sit above it.
Show solution
Approach: count the same step from the other end
- The two boys meet on one shared step on a staircase of 21 steps.
- Mike counts that step from the top: the steps above it plus the meeting step itself make up his count, which lands on the 11th.
- So Mike calls the meeting step the 11th — the answer is C.
Mark:
· log in to save