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Combinations and Permutations?
Suppose that you are able to take steps one, two, or three at a time. In how many different ways can you reach the top of 13 steps? (Hint: Find and apply a recursion relation)
1 Answer
- M3Lv 79 years agoFavorite Answer
let N_k be the # of ways to climb k stairs.
N_1 = 1 (1)
N_2 = 2 (1+1, 2)
N_3 = 4 (1+1+1,1+2, 2+1, 3)
for more than 3 steps, if the first step is 1,2 or 3, the # of ways of climbing the remaining stairs is N_(k-1), N_(k-2), and N_(k-3) resply, ie
N_k = N_(k-1) + N_(k-2) + N_(k-3)
so start with 1,2,4 and add the last three #s to get each succeeding #
1 (N_1)
2
4
7
13
24
44
81
149
274
504
927
1705 (N_13)
