## Friday, November 6, 2009

### A Dangerous Weekend Retreat

Kim and two of her girlfriends went for a weekend retreat in Western MA. After a swim, a sauna, a facial and a chocolate body wrap, they decided to take a short nap before dinner. Turned out that the facial lotion that was used on this day had some delayed chemical reaction when combined with the remainder of a chocolate, leading to strange blue spots on the faces of all three friends. When they woke up, each of them looked at her friends in bewilderment, assuming that they just painted their faces. Kim, being an expert in logical reasoning, was the first to realize that her face is as blue as her friends' faces. How did she do it?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Claire said...

Her friends were looking at her the with the same shock/amusement that she was looking at them.... or one of her friends was wearing glasses and she saw her reflection in them. Either way...

Maria said...

Hey, Claire! The glasses are a great idea. But I am not sure either of Kim's friends wears them. I think she used some deduction, as she always does. A hint: there is one puzzle that we solved long time ago in this puzzle marathon that she probably have read and it gave her an idea....

D.M. said...

Here's one scenario: If either of her friends only saw one blue face, they might be more worried and say something, because it would seem more like a disease or other affliction. However, since everybody sees two painted faces, it would be easier to assume they painted their faces as part of their party. So since neither of Kim's friends say anything in concern for the other friend, she assumes they must both see two blue faces.

Maria said...

D.M. - you are on a right track. But we should take it one step further on the "she assumes that her friend thinks" ladder of logic. It is a tricky puzzle.

Kim said...

This never would have happened. I would have eaten the chocolate before I had my body wrapped in it.

W said...

This puzzle reminds me of another one whose solution I'm trying to manipulate into working for this one, but perhaps unsuccessfully.

The puzzle that this reminds me of is the puzzle of a village with husbands and wives. We know that at least one husband is unfaithful but we do not know who. If a husband is ever found out to be unfaithful, they have to go to the center and announce it to the whole village.

Nothing happens for a while but one day, a psychic comes and says to the whole village "at least one husband is unfaithful".

What happens?

In any case, I am thinking that Kim realized that her friends assumed they painted faces because all of them had blue faces. If Kim was the only one without a blue face, Kim would realize that her friends wouldn't have assumed that they all painted their faces and that instead, something was wrong.

Tricky! And I'm now lost in my own logic :P

Maria said...

A puzzle for a puzzle. Very cool!
Let's count it only if strategies for solving both puzzles are the same. And I am not sure yet that they are.
Let's solve one and then another and see.
I am giving one more day for the above puzzle about Kim. Can you do it? Yes, you can!
There is a puzzle about three men arguing who is the smartest one that we solved 6 months or so ago that is very similar to the above puzzle about Kim...

Maria said...

Here is the solution:
Assume Kim's friends are named MaryAnn and Rachel. Kim wakes up and sees both of her friends' in bewilderment and with painted faces. She obviously assumes first that her face is perfectly clean. Then she thinks of what her friends are seeing and thinking. As Kim's face is presumably clean, then each of the friends should be seeing one painted and one clean face in front of them.

Therefore, MaryAnn sees Kim's clean face and Rachel's painted face. MaryAnn obviously assumes that her face is clean. But in this case Rachel would see two clean faces and won't have this shocking expression on her face. Since Rachel does appear shocked, MaryAnn can conclude that her face is not clean. But she doesn't.

We could apply similar logic to Rachel, saying that she should realize that her face is painted from the MaryAnn's expression. Rachel is also quiet.

So, Kim assumed that her face is clean and concluded that in that situation her friends should quickly realize that their face are painted. As neither of them did, Kim understood that her original assumption about her face being clean is wrong - it is painted!