Headline

A mathematical puzzle whose solution illustrates recursion

Citation

(https://en.wikipedia.org/wiki/Recursion_(computer_science), 10 November 2015)

There are three pegs which can hold stacks of disks of different diameters. A larger disk may never be stacked on top of a smaller. Starting with n disks on one peg, they must be moved to another peg one at a time. What is the smallest number of steps to move the stack?

Illustration

The following recursive function, given in Language:Java computes the smallest number of steps to move the stack.

public static int hanoi(int n) {
  if (n==1) 
    return 1;
  else 
    return 2 * hanoi(n-1) + 1;
}

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