Hosted by The Math Forum


Problem of the Week 845

How Not To Shuffle 351 Times

_____________________________________________
Fall 97 Archive || MacPOW Home || Math Forum POWs || Search MacPOW
_____________________________________________

Let fn denote the n-fold iterate of f. [That is, f0(x) = x, f1(x) = f(x), f2(x) = f(f(x)), and fn(x) = f(fn-1(x)) for all n>0.]

There is only one function f from {1, 2, 3, 4, 5, 6, 7} to itself such that f(x) = x for every x. On the other hand, there are 5040 such functions such that f5040(x) = x, namely all of them.

How many f are there such that f351(x) = x?

Source: Marcin Kuczma, Crux Mathematicorum, Nov. 1996

© Copyright 1997 Stan Wagon. Reproduced with permission.

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.

The Math Forum

2 October 1998