A simple logical question (Posted on 2007-07-27)

	Submitted by Praneeth
Rating: 3.3333 (3 votes)
Solution:	(Hide)
The given terms can be arranged in 12 different ways. So, 2 of the terms should be equal. y=d(y) has only two solutions 1,2. If one of the four terms x,d(x),d(d(x))and d(d(d(x))) is 1, it implies that all others are 1, but there is only 1 way to arrange these terms. So, x can not be 1. If you take x=2, then d(x)=2,d(d(x))=2 and so on. From this we can say that the last 2 terms must be equal for them to be arranged in 12 different ways. So, d(d(x))=2, this implies that d(x) is prime, which in turn implies that x has only 1 distinct prime factor. If n(x): no. of prime factors, then n(x)=p-1. (where p is odd prime) If n(x): no. of distinct prime factors, then n(x)=1. Possible values of x: 4,9,25,49,16,81,64 Note:If d(n,x)=d(d(...ntimes(x))), If n->infinity, Then d(n,x)=2 (if x is a positive integer other than 1)

	Subject	Author	Date
	re(2): computer exploration--lacking proof--spoilers	Charlie	2007-07-31 10:35:25
	re: computer exploration--lacking proof--spoilers	Praneeth	2007-07-30 09:15:42
	re: computer exploration--lacking proof--spoilers	rupesh	2007-07-27 18:34:15
	computer exploration--lacking proof--spoilers	Charlie	2007-07-27 12:13:58