# A staircase has 10 steps , you can walk up taking one or two steps at a time . how many ways can go up to top of stair ?

+2 votes
203 views
A staircase has 10 steps , you can walk up taking one or two steps at a time . how many ways can go up to top of stair ?
posted May 14, 2015
Share this puzzle

## 1 Answer

+3 votes

10C0 + 9C1 + 8C2 + 7C3 + 6C4 + 5C5
= 1+9+28+35+15+1
= 89

answer May 14, 2015
Sir , i didn't got your solution ,
my solution is of fibonacci series , like for 1step ==1 , 2nd step 1+1 or 2 ==2ways , 3rd step  1+1+1 or 1+2 or 2+1 ==3ways , so ,1,2,3,5,8,13,21,34,55,89 ,  for 10th step 89 ways .
I just tried for two three numbers and saw this logic is arriving (not sure why), but fibonacci  series is more logical :) thanks for asking great puzzle.
I am glad to be of help :)

Similar Puzzles
+1 vote

Garima takes the underground train to work and uses an escalator at the railway station. If Garima runs up 8 steps of the escalator, then it takes her 30.0 seconds to reach the top of the escalator. If she runs up 15 steps of the escalator, then it takes her only 12.5 seconds to reach the top.

How many seconds would it take Garima to reach the top if she did not run up any steps of the escalator at all?

0 votes

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

0 votes

Find amounts of money that can be made up in two ways so that one set of coins has twice as many coins as the other (but not using only 1c and 2c coins). e.g. 71c is 50c, 20c, 1c (3 coins) or 20c, 20c, 20c, 5c, 5c, 1c (6 coins)