Math
posted by Diana on .
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?

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 leftfooted
1 5 9 13 17 ... ( every 4th step)
step # when Charlene will be leftfooted
1 7 13 19 ... (every 6 steps)
first common number is 13