| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Newsgroups: net.math
Path: decwrl!decvax!mcnc!philabs!aecom!mpoppers
Subject: A Know/Don't Know Game
Posted: Mon Jun 4 11:16:37 1984
Two positive integers are chosen. The sum is revealed to logician A,
and the sum of squares is revealed to logician B. Both A and B are given this
information and the information contained in this sentence. The conversation
between A and B goes as follows, with B starting the dialogue:
B: "I can't tell what the two numbers are."
A: "I can't tell what the two numbers are."
B: "I can't tell what the two numbers are."
A: "I can't tell what the two numbers are."
B: "I can't tell what the two numbers are."
A: "I can't tell what the two numbers are."
B: "Now I can tell what the two numbers are."
WHAT ARE THE TWO NUMBERS?
-- problem composed by Tom Ferguson, UCLA
Michael Poppers at A.E.C.O.M.
{cucard,esquire,ihnp4,pegasus,philabs,rocky2,spike} | aecom | poppers,mpoppers
Summer USnail address: 143 Bennett Avenue-Apt. 3P
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 78.1 | HARE::STAN | Wed Jun 06 1984 23:38 | 3 | ||
This is problem 1173(a) from Mathematics Magazine 56(1983)177. Tom's solution is published in Mathematics Magazine 57(1984)180-181. | |||||
| 78.2 | HARE::STAN | Wed Jun 27 1984 23:45 | 43 | ||
Newsgroups: net.math
Path: decwrl!decvax!mcnc!unc!ulysses!mhuxl!ihnp4!zehntel!hplabs!hao!seismo!cmcl2!rocky2!cucard!aecom!mpoppers
Subject: Solution to the Know/Don't Know Game
Posted: Tue Jun 19 13:10:36 1984
After B's first announcement, the possibilities are reduced to a table
which begins as follows:
SUM SUM OF SQUARES
======= ==============
8 50
9 65
10 50
11 65,85
13 85,125,145
14 130,170
15 125
16 130,200
17 145,185,205
.... ....
The only appearances of 50, 65, 85, 125, and 145 as a sum of squares
in this table are already displayed. A's first announcement rules out the sums
8, 9, 10, and 15. B's second announcement rules out the 65 from the row of sum
11 and the 125 from the row of sum 13. A's second announcement rules out the
sum 11. B's third announcement rules out the 85 from the row of sum 13. A's
third rules out the sum 13. B's fourth announcement shows one
possible answer to be that the sum is 17 and the sum of squares 145, giving
8 and 9 as the numbers.
PART II COMING SOON!!!
{[][][][][][][][]}
{ PERITUS CLAVIS }
{ MACHINAE VIVIT }
{[][][][][][][][]}
Until June 30: Michael Poppers @ { XX } | aecom | mpoppers, where XX =
spike,rocky2,ihnp4,pegasus,esquire,cucard,philabs
| |||||
| 78.3 | Quid? Vexarae Mi? | KIRK::KOLKER | Wed Jun 10 1987 09:55 | 3 | |
re .2
What does peritus clavis machinae vivit mean?
| |||||