Re: How many ways can a boy go up a staircase?

>A staircase consists of 10 steps. A boy can move up to >a maximum of 3 steps in each hop. How many
> different ways can he walk/run/jump the staircase?

Taking the largest steps first to
keep it simple. Then find the combinations
possible for each group.

(4)steps (The least possible)

3331 = 4 combinations.
-----
(5)steps

33211 = 30 comb.
32221 = 20 comb.
22222 = 1 comb.
------
(6) steps.

331111 = 15 comb.
322111 = 46 comb.
222211 = 15 comb.
-------
(7) steps
3211111 = 42 comb.
2221111 = 35 comb.
-------
(8)steps
31111111 = 8 comb.
22111111 = 28 comb.
--------
(9) steps
211111111 = 9 comb.
---------
(10) steps
1111111111 = 1 comb.
---------
254 total combinations.

Dan
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