Posted by **jen** on Monday, September 27, 2010 at 9:30pm.

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 -
**Reiny**, Monday, September 27, 2010 at 10:14pm
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

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**huh**, Tuesday, September 28, 2010 at 6:57pm
...what?

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**karina**, Sunday, October 3, 2010 at 5:27pm
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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