Question:
Paul, Michelle and Michael all climb up 54 steps. Paul climbs the steps one at a time i.e. 1, 2, 3, etc. Michelle Climbs the stairs 2 at a time i.e. 2, 4, 6, etc. Michael climbs the stairs 3 at a time i.e. 3, 6, 9, etc. How many steps are used by exactly two people?

Hi Harman,

Paul uses every step.

Michelle uses the steps that are divisible by 2. Thus Paul and Michelle use the steps that are divisible by 2. How many of these are there?

Michael uses the steps that are divisible by 3. Thus Paul and Michael use the steps that are divisible by 3. How many are there?

Some steps are used by all three. These are the steps that are divisible by both 2 and 3, that is the steps that are divisible by 6. How many are there?

Thus the number of steps that are used by exactly two people is

   (the number of steps used by Paul and Michelle)
+ (the number of steps used by Paul and Michael)
-  (the number of steps used by all three)

Cheers,
Penny