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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 -

    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

    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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