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" ... Here it goes. Let n be a positive integer and define a function f by the rule f(n) = n/2 if n is even and f(n) = (3n + 1)/2 if n is odd. Since the output of f is another positive integer, you can apply f to the result, and then apply f to that result, and so on. Say you do this k times; denote the result by fk(n). The Collatz Conjecture is that for every positive integer n, there is some k with fk(n) = 1. Simple, right? ... "