The Towers of Hanoi and Binary Numerals
M. C. Er · Journal of Information and Optimization Sciences · 1985
An interesting relation between the Towers of Hanoi and the binary numerals is proved; that is, the disc to be moved in step x is precisely the position of the rightmost 1 in the binary repressntation of x, if the discs are numbered 1, 2, 3, …, n from the smallest to the largest. A simple iterative algorithm for solving the Towers of Hanoi problem is also presented, using the above relation. Finally, an observation concerning the iterative programming is made.