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 The Two Logicians (Posted on 2003-04-11)
Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues:

A: "I don't know my number."

B: "I don't know my number."

A: "I don't know my number."

B: "I don't know my number."

........ n statements of ignorance later..........

A or B: "I know my number."

What is on the card and how does the logician know it?

 Submitted by Ravi Raja Rating: 2.5556 (9 votes) Solution: (Hide) If A saw 1, he would know that he had 2, and would say so. Therefore, A did not see 1. A says "I don't know my number." If B saw 2, he would know that he had 3, since he knows that A did not see 1, so B did not see 1 or 2. B says "I don't know my number." If A saw 3, he would know that he had 4, since he knows that B did not see 1 or 2, so A did not see 1, 2 or 3. A says "I don't know my number." If B saw 4, he would know that he had 5, since he knows that A did not see 1, 2 or 3, so B did not see 1, 2, 3 or 4. B says "I don't know my number." ........ n statements of ignorance later ........ if X saw n, he would know that he had n + 1, since he knows that ~X did not see 1 ... n - 1, so X did see n. X says "I know my number." And the number is n + 1.

 Subject Author Date HA Chaz 2003-05-03 04:04:42 My Nitpicking Note Charlie 2003-04-11 08:33:10 My attempt Ender 2003-04-11 06:37:44 re: Attempt Jon 2003-04-11 06:21:55 Attempt DJ 2003-04-11 05:50:45 ummm........... Jon 2003-04-11 05:44:44

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