# 6 people racing down a flight of steps

doodinthemood
Posers and Puzzles 31 Oct '07 07:34
1. 31 Oct '07 07:34
Paul lands on every step, Bob lands on every 2 steps, Chris lands on every 3 steps, Charlie lands on every 4 steps, Sam lands on every 5 steps, Jack lands on every 6 steps.

There are only two occasions where they all land on the same step - the first step, and the penultimate step.

How many steps did they race down?
2. TheMaster37
Kupikupopo!
31 Oct '07 08:41
Originally posted by doodinthemood
Paul lands on every step, Bob lands on every 2 steps, Chris lands on every 3 steps, Charlie lands on every 4 steps, Sam lands on every 5 steps, Jack lands on every 6 steps.

There are only two occasions where they all land on the same step - the first step, and the penultimate step.

How many steps did they race down?
Quite an easy problem if you know how to see it ðŸ™‚
3. 31 Oct '07 13:52
My immediate instinct is that they must "meet" every 60 steps (60 being the lowest number divisible by 2...6**). Then meeting on step 1 means the penultimate step where they next meet is step 61, so there are 62 steps?

** (1x2x3x4x5x6)/(2x2x3)
4. 01 Nov '07 03:51
Depending on the reading of your question 62 is the number which you seem to be trying to get at, but the English would lead to the solution 3.

If everybody steps on every n steps then they all stepped on the second step too. However the second guy would not step on the third step so they only all stepped on two steps.
5. wolfgang59
Mr. Wolf
01 Nov '07 18:43
Originally posted by doodinthemood
Paul lands on every step, Bob lands on every 2 steps, Chris lands on every 3 steps, Charlie lands on every 4 steps, Sam lands on every 5 steps, Jack lands on every 6 steps.

There are only two occasions where they all land on the same step - the first step, and the penultimate step.

How many steps did they race down?
Presumably by 'first step' you mean where they start (really step '0'ðŸ˜‰. As others have said they meet again after 60 steps which is the penultimate so answer is 61.
6. 02 Nov '07 03:08
Originally posted by Gastel
Depending on the reading of your question 62 is the number which you seem to be trying to get at, but the English would lead to the solution 3.

If everybody steps on every n steps then they all stepped on the second step too. However the second guy would not step on the third step so they only all stepped on two steps.
three out of the five people skip step two and three so how would they meet on the second step.