## Friday, October 5, 2012

### Solution to Liar, Liar

Dear Puzzlers,

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And now onto the solution.  Please remember, this particular puzzle had nothing to do with solving for a a number.  Your task was to identify the liar.  Lets' restate the problem:

Four friends make statements about a number

Andrew: It has two digits

Barbara: It goes evenly into 150

Cindy: It is not 150

Daniel: It is divisible by 25.

One more thing there is exactly one liar, no more, no less.

Our Solution:
By cases - Andrew: Suppose Andrew is the liar and the number has either one digit or more than two.  If it has one digit, then Daniel is a liar also since it cannot be divisible by 25.  If it is three or more digits then Barbara is a liar since it can't go evenly into 150

Therefore Andrew is not a liar!!!!

Barbara: Suppose Barbara is the liar, then our number does not go evenly into 150.  Then either Andrew or Daniel is a liar.  The two digit multiples of 25 are 25, 50, and 75 all of which  go evenly into 150.

Therefore Barbara is not a liar!!!!

Cindy:  Suppose Cindy is the liar.  Then the number is 150.  Then Andrew is a liar since the number has more than two digits.

Therefore Cindy is not a liar!!!!

Daniel:  Suppose Daniel is the liar.  Then our number is not divisible by 25, say 15.  It is easily shown that each of the other three are telling the truth.

Daniel is a lying Punkbaby!!!