Who committed the murder? (Posted on 2008-10-08)

	Submitted by pcbouhid
Rating: 3.0000 (1 votes)
Solution:	(Hide)
Let x -> y to mean that x was charged with the crime y. Of course, crimes and criminals have the same names, so that x -> y -> z means that x was charged with the crime called y, and the criminal y was charged with the crime z. Notice that x -> x is never true, as was stated in the problem. The next sentence of the problem is a little hard to work out, but it ultimately comes down to B -> x -> y -> M and the sentence following is exactly parallel: M -> z -> w -> F. Now, if we consider the five crimes/criminals, starting with, say, B, and looking at the sequence B -> x1 -> x2 -> x3 -> x4 -> ... we should find that the sequence repeats. There are only five crimes (or five criminals) so some two x's will be the same. Then the sequence between them will repeat. Furthermore, since each crime was only charged to one criminal, the sequence repeats backward to the B as well. This is a cycle, and the length of the cycle cannot be one, since no criminal was charged with his namesake. That leaves two possibilities: a) Either two criminals were charged with one another's namesake (a cycle of length two) and the other three form a cycle of length three, or b) there is only one cycle of length five. (Of course, we can't have a cycle of length four, since the leftover criminal would have to be charged with his namesake.) But: B -> x -> y -> M and M -> z -> w -> F means that B, M, and F cannot be in a cycle of length three. There are only two other criminals left, which isn't enough for a cycle of length three. That means that the first possibility is not possible, so there is only one cycle of length five. So that means that we have B -> x -> y -> M -> z -> B with the cycle being (B, x, y, M, z). But then M -> z -> w -> F means that w = B, and F = x, so that our cycle is B -> F -> y -> M -> z -> B. Now it only remains to determine y and z. We want to find out who was charged with murder (and therefore convicted), which means who is y? y was placed on death row, which means that y is not Theft, because Theft got seven years. So that means that z is Theft, and the only remaining criminal is Libel, who must be the murderer y. B -> F -> L -> M -> T -> B, and we conclude that: Blackmail was charged with fraud, Fraud was charged with libel, Libel was charged with murder, Murder was charged with theft, and Theft was charged with blackmail.

	Subject	Author	Date
	Puzzle Answer	K Sengupta	2022-05-16 22:37:01
	No Subject	Linda Ween	2020-05-06 05:40:23
	re: Solution	edward	2019-06-25 01:14:09
	Solution	rod hines	2008-10-10 15:28:45
	Solution	Tristan Nieto	2008-10-09 12:36:26
	re: Solution	Daniel	2008-10-08 13:09:52
	Solution	Dej Mar	2008-10-08 12:35:48
	Solution	Robby Goetschalckx	2008-10-08 12:35:13