Friday Puzzler -- forehead dots

Re: Friday Puzzler -- forehead dots

John Langley

Nobody goes anywhere

Re: Friday Puzzler -- forehead dots

Larry Barrett

Suppose there are just 2 logicians, A and B. A would think this way:

If I have a red dot, then B would know that he has a blue dot and would leave after the first bell. If B does not leave, that must mean that B sees a blue dot. So A would then leave after the second bell. B would follow the same reasoning and would also leave after the second bell.

Now suppose there are 3 logicians, A, B, and C.

A starts off the same way: Suppose I (A) have a red dot. He then watches C. A would think that if C thought he (C) also had a red dot (and if A has a red dot), then B would know he had a blue dot and would leave after the first bell. If B does not leave, C would know he had a blue dot and would leave after the second bell. So A would know that if neither B nor C leave, he (A) must have a blue dot and would leave after the third bell. B and C would follow the same reasoning and would also leave after the third bell.

So I think by analogy that with 100 logicians, no one would leave after the first 99 bells, but all would leave after the 100th bell.

Good start

Alex Y

And correct for a while.

Correct!!

Alex Y

Induction in action.

Nice job.

A more impossible-sounding puzzle that yields to the same solution method: The logicians each have a number on a sticker on their forehead. No restriction on what the number might be, e.g. 2, pi, 7+3i, etc. They are to leave when they figure out the number on their own forehead. Only other information they are given is that all of them can eventually leave. How does that work?