Sorry. I mentioned the book in an earlier message. "Tracking the Automatic Ant and othe mathematical explorations", Springer, 199?.

DG You wouldn't believe what you get when you are searching for David Gale on

Amazon ("The Life of David Gale" included!). What is the name of your book?

Helger

On Mon, 5 Jan 2004, David Gale wrote:

...

Here are some more subtle examples.

1.You and I have numbers on our foreheads and are told (truthfully) that their total is either 5, 8 or 15. A bell rings every ten seconds and after each ring if either of us knows our number we announce it and win. Prove: For any pair of forehead numbers one of us will know our number after at most 10 rings. (Curiously, if the numbers are 5,9,15 then the bell can ring until the cows come home and there will be no winner).

2. (Conway-Paterson) In the three player game with forehead numbers 2,2,2 and possible totals 6,7,8 the players will know their numbers after on the 15th ring.

To see why buy my book. (Amazon usually ships in 24 hours)

David

At 04:52 PM 1/5/04 -0800, you wrote:

...

As it was originally told to me . . .

A traveler passes through a small village, each of whose inhabitants has a single colored dot on his or her forehead. Some have a blue dot, some have a red dot, some have a green dot, etc. Each person can see every other person's dot, but cannot see his own. Because the village is small, every person knows the color of every other person's dot, except his own. It is taboo in the village to know the color of one's own dot. The village's strict rule is that anyone discovering the color of his own dot must leave the village within 24 hours, never to return. As the traveler passes through, he casually remarks, "Some people in this village have blue dots". Ten days later, the ten people from the village who had blue dots have all vanished.

The problem is to explain how the departure of the ten people occurred.

JSS

asimovd@aol.com wrote:

...

Scott asks:

<< ... Then two mathematicians iterate for awhile, A: I can't deduce the answer. B: Neither can I. A: I still can't deduce the answer. ...

and after a few rounds of this one of them can deduce the answer.

Can anyone supply some puzzles of this flavor? (without answer :-)

...

...

I vaguely recall one of this type (in a 1958 book, "Puzzle-Math", by G. Gamow & M. Stern) which concerned determining which wives were cheating on their husbands, but I can't recall the details -- except that it took 40 days to deduce who the cheaters were.

The book is, I fear, out of print, but many local libraries may have copies.

Dan Asimov

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