perplexus.info :: Logic : Two Logicians Lockout

Two Logicians Lockout (Posted on 2007-03-13)

Two different integers from 1 to N are chosen. Sam is given the sum and Pat is given the product. Sam and Pat take turns stating whether they can determine the numbers

Sam: I don't know the numbers.
Pat: I don't know the numbers.
Sam: I don't know the numbers.
Pat: I don't know the numbers.
.
.
.
.
Sam and Pat continue like this until one of them realizes that it is impossible for either of them to determine the numbers. What is the smallest possible N for which this can happen?

Submitted by Brian Smith

Rating: 4.0000 (1 votes)

Solution: (Hide)

N=12 with numbers:
X Y S P 1 10 11 10 1 12 13 12 2 5 7 10 2 12 14 24 3 4 7 12 3 8 11 24 3 10 13 30 4 10 14 40 5 6 11 30 5 8 13 40

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2024-01-31 06:38:23
what about 1	Fox	2007-03-27 01:53:19
Graphical interpretation (examples)	Gamer	2007-03-18 17:01:00
Graphical interpretation (word explanation)	Gamer	2007-03-18 16:46:56
re: ...Huh?	Charlie	2007-03-18 15:00:07
...Huh?	George	2007-03-18 11:44:30
real computer solution -- disregard previous	Charlie	2007-03-14 09:40:21
re: computer solution -- more	Charlie	2007-03-14 09:13:38
computer solution	Charlie	2007-03-14 09:04:00
More than 30 seconds.	Leming	2007-03-14 07:25:20

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