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        riddles >> easy >> Logical Signs II
        
(Message started by: potter on Jul 29^th, 2002, 3:03am)

Title: Logical Signs II
Post by potter on Jul 29^th, 2002, 3:03am

This one seems simpler than logical sign I. There are 6 possible cases of True and False for the three chests. 4 of them are contradictory as in each one of them point to more than one chest as containing the treasure. The rest 2 cases both point towards the BRONZE one. so the treasure lies in the BRONZE chest.

These 2 cases are: Silver - false false
Gold - true true or false
Bronze- true or false true

Title: Re: Logical Signs II
Post by jc on Aug 3^rd, 2002, 11:23pm

Well, I got the same answer, only I found only one of the six possible answers pointing to bronze.

The six were:

1: S - True, G - False, B - False

Which wouldn't work because G and B both being false mean that the treasure is in G, and yet S is also true. Since the treasure is only in one, this possibility becomes impossible.

2: S - True, G - True, B - False

Which wouldn't work because G and B contradict each other.

3: S - True, G - False, B - True

Which wouldn't work because G and B contradict each other.

4: S - False, G - True, B - False

Which wouldn't work because G and B contradict each other.

5: S - False, G - False, B - True

Which wouldn't work because G and B contradict each other.

6: S - False, G - True, B - True

Which is the only solution that works out, and it points to B, since S being false means the treasure isn't in S and G and B being true means that it's not in G.

So, 4 contradictions, one case of the treasure being in 2 chests, and one solution that works. :P

I admit this was an awfully methodical way to do it, and you could shorten it by quite a bit by assuming that S must be false in the "true" solution because you can infer that all three possibilities with S being true must be ruled out without actually listing them. Still, it worked.

Title: Re: Logical Signs II
Post by Melkor on Aug 5^th, 2002, 9:06pm

There is an easier approach: begin by assuming that the silver chest holds the treasure. Then check the resultant veracity of the chests' labels against the known information - i.e., that at least one chest's label is true and at least on is false. Thus the silver chest cannot contain the treasure since then all three statements would be true. Continue with the other chests until you find an assumption that fits the given information.

Title: Re: Logical Signs II
Post by Icarus on Oct 8^th, 2002, 7:50pm

Usually, the best way to solve a logic problem is by examining the cases and using them to evaluate the statements. Not only is it often easier, but you can more easily avoid the mistake of assuming a statement has to be true or false. It can also be a contradiction (true if it is false, and false if it is true) or indeterminate (true only if it is true, and false only if it is false). This problem does not have that situation, but it is very big in Logical Signs I.