You have three small poles and five hoops - XS, S, M, L, XL (as in extra small, small, medium, large and extra large). They are placed on pole 1 in order, with largest at the bottom.

You can move one hoop at a time, and the hoops you are not moving have to be on a pole. You also cannot place a hoop on top of a smaller one. How can you move the hoops so that they are in the same order as they are now, but on pole 3?

(In reply to strategy by Charlie)

I don't think your numbers at the bottom are correct. I think they should be powers of 2 minus 1 By induction (which I am not so good with), the n(1) = 1, and the n(x+1)=2(n(x))+1, but this can be expressed this way as well:

n(1) equals 2^1-1,
n(2) equals 2(2^1-1)+1 = 2(2^1)-1 =2^2-1
n(3) equals 2(2^2 - 1) + 1 = 2^3 - 1
So if (n(x) equals 2^x - 1, then n(x+1)=n(x)+1 = 2(2^x -1) +1 = 2^(x+1)-1

Posted by Gamer on 2003-09-07 14:15:48