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When I first attempted this puzzle I tried finding a pattern in the possible ways of going up a smaller no. of steps. I used the binary system to find all the possible ways . Finally I got the formula: 2 to the power of n! Then I did 2 to the power of 10 (the no. of steps) and got 1024 (no. of ways to go up 10 steps). Then I checked the solution and found mine was wrong!! I don't understand what I did wrong!? Can somebody please explain??

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