A Statement to Save a Life
Date: 05/28/97 at 12:17:43 From: Ray Subject: How can this man save his life? A man is lost in a forest and is trying to find his way out when he is found by a group of cannibals. The cannibals take him to their village and tell him that he can make one statement that will determine how he will die. They tell him that if he tells a lie, he will die by poison and that if he tells the truth he will die by the bullet. What statement will save his life?
Date: 05/29/97 at 19:14:41 From: Doctor Keith Subject: Re: How can this man save his life? Dear Ray, Fun problem! We can write down our information in table form: Statement is | Death by =================|============ True | bullet -----------------|------------ False | poison We need to find a statement that will make their statement wrong if they carry it out. Then presuming they are honorable, they cannot act (i.e., kill the traveller). It sounds good, but what does it mean? Well, we need to make our statement false if the man dies by a bullet and true if the man dies by poison. So the man tries the following: "You will kill me by poison." Then let's see what happens. We have two cases to consider: 1) They shoot him. Then his statement was false, so if they were honorable, they would have poisoned him, so they cannot shoot him and be true to their word. 2) They poison him, thus he said a true statement and should have been shot. Thus to poison him goes against their word, and they cannot do it. Thus they must let him live! So we have a statement that works. Of course we are assuming that the cannibals are all-knowing, otherwise a statement like "My mother's name is Jen" would be a problem. In theory, your typical cannibal does not know the man's mother's name, so the validity of the statement is unknown. Thus to act could violate the cannibals word, and they supposedly won't do that. This brings up the whole area of unanswerable questions and statements that are not true or false. The command, "Eat your lunch" is neither true nor false in any circumstance, so what do they do? This situation is not defined in the problem. Of course they could get tricky and poison the bullet to handle this. Why do I mention all this? Well there is an obvious best answer: "You will kill me by poison." But even given what seems a completely stated problem with a best answer, there are special cases where things fall apart. This is true in many areas of math and life in general and you just want to be on the lookout for how things can fail. In other words, when you first see a problem, read carefully and try to see whether something has not been stated clearly enough or where the problem lies. Also note there is often ambiguity going from English (or any language) to math, and many problems like this come up from these issues. If these type of problems interest you, I suggest you look into what is called logic. I used an arguement in mathematical logic to get the best answer and to test it out. There are many great problems like this one out there so you can have lots of fun and develop very practical skills for later life. If any of this is confusing let me know which part and I will clarify it. Hope all of this helps. -Doctor Keith, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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