Question

Bob and Sue are meeting on a stairway. Bob is at the top and Sue is at the bottom. There are 9 steps

from bottom to top. Bob can skip a step each time since he is going down, Sue will not skip any steps. On
which step will they meet.

Answer 1

Bob is at the top, so he starts at step 9.

Sue is at the bottom, so she is at the step 0 (this is the floor, before stepping on step 1)

Sue climbs from one step on one step.

Then she if she climbs n times, she will be at the step number:

S(n) = 0 + 1*n

And Bob goes down by 2 steps each time, then after he goes down n times, his position will be:

B(n) = 9 - 2*n

We want to see when they meet, then we need to solve:

S(n) = B(n)

1*n = 9 - 2*n

1*n + 2*n = 9

3*n = 9

n = 9/3 = 3

n = 3.

This means that they meet a the step:

S(3) = 3*1 = 3

B(3) = 9 - 2*3 = 9 - 6 = 3

They meet at the third steep.