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An elf has a staircase with 10 steps to climb. Each step it takes can cover either one stair or two stairs. In how many ways can the elf climb the stairs?

  • math -

    5 Doubles === 1 way
    4 Doubles, 2 Singles === e.g. DDSSDD
    number of ways = 6!/(2!4!) or C(6,4) = 15
    3 Doubles, 4 Singles === C(7,3) = 35
    2 Doubles , 6 Singles === C(8,2) = 28
    1 Double , 8 Singles === C(9,1) = 9
    10 Singles === 1

    total = 89

  • math -

    ...what?

  • math -

    i don't understand how its 89 ways!
    how about 20 stairs, and N stairs? what would be the equation for that?

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