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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

**, no more, no less.**

__exactly one liar__**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!!!**

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