Posted by **Diana** on Tuesday, May 17, 2011 at 8:39am.

Alice, Beth, and Charlene start climbing a staircase, each with her left foot on step 1 and then her right foot on the next consecutive step. Alice climbs one step at a time, Beth two steps at a time, and Charlene three steps at a time. Each lands on the top step with her left foot. Compute the minimum number of stairs in the staircase.

I'm not sure how to do this. Should i set up equations?

- Math -
**Reiny**, Tuesday, May 17, 2011 at 8:52am
How about making a chart, with 4 columns

# A B C

1 L L L

2 R - -

3 L R -

4 R - R

5 L L -

6 R - -

7 L R L

8 R - -

9 L L -

10R - R

11L R -

12 R - -

13 L L L , AHHH, all left feet on 13th step

or

step # when Alice will be left footed

1 3 5 7 9 11 13 15 ... (every 2nd step)

step # when Beth will be left-footed

1 5 9 13 17 ... ( every 4th step)

step # when Charlene will be left-footed

1 7 13 19 ... (every 6 steps)

first common number is 13

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