[math-fun] looking for state-of-knowledge logic puzzles
I'm looking for one or more logic puzzles I've seen in the past that run something like the following: Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product. 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 :-) Thanks, - Scott P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer". I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
See p.305, Logic problems, of Paul Vaderlind, Richard Guy & Loren Larson, The Inquisitive Problem Solver, MAA Problem Books, 2002 where some other references are given. R. On Mon, 5 Jan 2004, Scott Huddleston wrote:
I'm looking for one or more logic puzzles I've seen in the past that run something like the following:
Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product.
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 :-)
Thanks, - Scott
P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer".
I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Scott and Richard, You will also find a bunch of puzzles of this flavor in chapter 15 of my book "Tracking the Automatic Ant" the nicest one being the so-called Conway-Paterson game. At 02:45 PM 1/5/04 -0700, you wrote:
See p.305, Logic problems, of
Paul Vaderlind, Richard Guy & Loren Larson, The Inquisitive Problem Solver, MAA Problem Books, 2002
where some other references are given. R.
On Mon, 5 Jan 2004, Scott Huddleston wrote:
I'm looking for one or more logic puzzles I've seen in the past that run something like the following:
Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product.
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 :-)
Thanks, - Scott
P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer".
I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The original reference here is A headache-causing problem, presented to Hendrik W. Lenstra Jnr on the occasion of his doctoral examination. Conway (J.H.), Paterson (M.S.), and Moscow (U.S.S.R.) in Een Pak Met Een Korte Broek, Amsterdam, 77-05-18. As this won't be easily accessible to most readers, I quote the Abstract: After disproving the celebrated Conway-Paterson-Moscow theorem, we prove that theorem and make an application to a well-known number-theoretical problem. R. On Mon, 5 Jan 2004, David Gale wrote:
Scott and Richard, You will also find a bunch of puzzles of this flavor in chapter 15 of my book "Tracking the Automatic Ant" the nicest one being the so-called Conway-Paterson game.
At 02:45 PM 1/5/04 -0700, you wrote:
See p.305, Logic problems, of
Paul Vaderlind, Richard Guy & Loren Larson, The Inquisitive Problem Solver, MAA Problem Books, 2002
where some other references are given. R.
On Mon, 5 Jan 2004, Scott Huddleston wrote:
I'm looking for one or more logic puzzles I've seen in the past that run something like the following:
Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product.
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 :-)
Thanks, - Scott
P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer".
I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The next book has a lot of puzzles of this favour and also a theoretical analysis of these: R. Fagin, JY Halpern, Y Moses and MY Vardi. Reasoning about Knowledge. The "muddy children" puzzle is the most famous one. For me personally it would be interesting to see any such puzzles where one or both participants are polynomially-bounded (i.e., involving factoring). Does anybody know any? Helger On Mon, 5 Jan 2004, Scott Huddleston wrote:
I'm looking for one or more logic puzzles I've seen in the past that run something like the following:
Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product.
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 :-)
Thanks, - Scott
P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer".
I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
David Gale -
Helger Lipmaa -
Richard Guy -
Scott Huddleston