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.

Question

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?

Reiny · Answer

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