## Tuesday, January 19, 2010

### Quick and Easy Logic About the Smiths

Mr. and Mrs. Smith and their two children form a typical American family. If exactly two of the following statements are true, what is the first name of the father, mother, son and daughter:
• George and Dorothy are blood relatives.
• Howard is older than George.
• Virginia is younger than Howard.
• Virginia is older than Dorothy.

1. Father : Howard
Mother : Virginia
Son : George
Daughter : Dorothy
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2. I have the same answer but I don't understand how any of the statements are untrue, all of the information points to the same answer whatever 2 statements you use....

3. Father : Howard
Mother : Virginia
Son : George
Daughter : Dorothy

4. I have a different answer.

I think only statements 2 and 3 are correct.

Father: Howard
Mother: Dorothy
Son: George
Daughter: Virginia

The first statement plants an idea in your head that is hard to steer away from, but if George and Dorothy aren't the kids, it is easier to figure out.

5. If 1 and 2 are true, that means George and Dorothy are not both parents, and Howard is the father. But that means 3 and 4 cannot be true. If 3 is false, then Virginia is the mother. But that means 4 is true, so 1 and 2 cannot be true.

Suppose 1 is false. Then George and Dorothy are the parents. This means that 2 is also false, since George would be older than his son Howard. 3 could be true, since Virginia could be Howard's younger sister, but that means 4 is false. So that doesn't work.

So, 1 must be true, and 2 must be false. If 2 is false, then George is the father. For one to be true, then Virginia is the mother. 3 has to be false because Virginia must be older than her son Howard. 4 must be true, since Virginia would be older than her daughter Dorothy.

6. If one was false, it would violate two of the other statements so it has to be true. If one is true, pick any of the other two statements, then see if the other two are false, if any of the other two are true then that violates the exactly 2 rule so that one can be crossed off.

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