## Thursday, May 20, 2010

### Doctor's Dilemma

Three sisters - Hannah, Hope and Hillary - are identical triplets. However, while Hannah always tells the truth, Hope always lies, and Hillary is only occasionally truthful.

All three sisters came to the doctor's office but only Hope needed to get her influenza shots. Confused to see three identical faces, doctor asked the sister that was sitting on the left, "Which sister is in the middle of you three?" and the answer he received was, "Oh, that's Hannah."
Then he asked the sister in the middle, "What is your name?" The response given was, "I'm Hillary." Confused, he turned to the sister on the right, then asked, "Who is that in the middle?" The sister then replied, "She is Hope."

Frustrated to receive three different answers to the same question, doctor turned to logic. Can it help him figure out which sister to take for the shot?

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Dennis said...

Number the girls left to right as 1, 2, 3.

Assume #1 is telling the truth. Then #2 is Hanna and #1 is Hillary. But - #2 says she's Hillary, which would be a lie if she's Hanna, which she can't do. So, #1 is lying and must be Hope or Hillary.

Assume #2 is truthful. She's Hillary, who can tell the truth. Since #2 is Hillary, #1 must be Hope (see above). That makes #3 Hanna... but #3 says #2 is Hope, which is a lie, and Hanna can't lie. Therefore, #2 must also be lying.

Since #1 and #2 are lying, #3 must be Hanna. Since Hanna tells the truth, #2 must be Hope and #1 must be Hillary.

Maria said...

Right on, Dennis! Take the middle sister for the shot. Did you read Sherlock Holmes growing up?

Lynnet said...

the first statement could not have been said by Hannah because that would be a lie.
the second statement could not have been said by Hannah because that would be a lie.
the third statement has to have been said by Hannah because she needs to answer and has not yet answered the question.

Lynnet said...

the first statement could not have been said by Hannah because that would be a lie.
the second statement could not have been said by Hannah because that would be a lie.
the third statement has to have been said by Hannah because she has not yet answered the question and needs to give an answer.

Anonymous said...

I'm 11, and I got the same answer as Dennis. YAY!