Comments on: Salem witches – a math puzzle

By: Mutual vs Common Knowledge in course difficulty - Mind Your Decisions

Mutual vs Common Knowledge in course difficulty - Mind Your Decisions — Thu, 10 Mar 2011 08:36:43 +0000

[...] The two concepts are very similar but not identical. There are fun ways to understand the distinction, and I have written about two puzzles that illustrate: Guess the number – a game theory puzzle, and Salem Witches – a math puzzle. [...]

By: Travels in a Mathematical World

Travels in a Mathematical World — Fri, 02 Jul 2010 10:13:06 +0000

Carnival of Mathematics #67…

Meanwhile, over at Mind Your Decisions, Presh Talwalkar discusses solutions for another of James’ YouTube puzzles in Salem witches Â– a math puzzle….

By: Jouvent

Jouvent — Fri, 25 Jun 2010 17:20:07 +0000

Hy,
Very interesting problem for sure.
But it can be generalized to more than two people and more than to colors…

As long as there is the same number of people and colors there is a strategy to pass the test.

By: michael webster

michael webster — Fri, 25 Jun 2010 01:05:19 +0000

I still have to disagree with Presh.

But this is a fundamental disagreement – it focuses on what we can expect from a calculation versus a recommendation for action.

The previous commentators, quite smartly I thought, pointed out that the problem was underdescribed.

Presh then added to the problem description the ability of the participants to talk for a minute to discuss strategy.

But if they can talk for a minute, they can simply agree on how to coordinate their guesses. Which makes the problem trivial.

What makes this interesting as a problem is to find the conditions which would make Presh’s calculations a focal point and not my idiosyncratic observations the focal point – that is who looks like a red/blue witch.

We are all better of with markets that allow calculations rather than stories for coordination, but it is not at all obvious how we manage to do achieve this.

By: Presh Talwalkar

Presh Talwalkar — Thu, 24 Jun 2010 19:53:35 +0000

Thanks all for the comments. I added a sentence that the witches can discuss strategy before the game which will allow them to designate who is player 1 and 2.

Second, the players are guessing the other person’s card. So in the scenario “1 gets blue, 2 gets red â€“>1 guesses blue, 2 guesses blueâ€“> 1 is wrong and they win” player 1 is guessing that player 2 is holding a blue card which is wrong. That’s why player 1 is wrong and they win. Sorry it is convoluted–I will think of a better way to present it.