This is probably well-known.
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
I don't know, but I bet it involves one of these:
I don't know, but I bet it involves one of these
I don't know, but I bet it involves one of thes
I don't know, but I bet it involves one of the
I don't know, but I bet it involves one of th
I don't know, but I bet it involves one of t
I don't know, but I bet it involves one of
I don't know, but I bet it involves one of
I don't know, but I bet it involves one o
I don't know, but I bet it involves one
I don't know, but I bet it involves one
I don't know, but I bet it involves on
I don't know, but I bet it involves o
I don't know, but I bet it involves
I don't know, but I bet it involves
I don't know, but I bet it involve
I don't know, but I bet it involv
I don't know, but I bet it invol
I don't know, but I bet it invo
I don't know, but I bet it inv
I don't know, but I bet it in
I don't know, but I bet it i
I don't know, but I bet it
I don't know, but I bet it
I don't know, but I bet i
I don't know, but I bet
I don't know, but I bet
I don't know, but I be
I don't know, but I b
I don't know, but I
I don't know, but I
I don't know, but
I don't know, but
I don't know, bu
I don't know, b
I don't know,
I don't know,
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I don't kno
I don't kn
I don't k
I don't
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Richard Heathfield submitted this idea :
I don't know, but I bet it involves one of these:
I don't know, but I bet it involves one of these
I don't know, but I bet it involves one of thes
I don't know, but I bet it involves one of the
I don't know, but I bet it involves one of th
I don't know, but I bet it involves one of t
I don't know, but I bet it involves one of
I don't know, but I bet it involves one of
I don't know, but I bet it involves one o
I don't know, but I bet it involves one
I don't know, but I bet it involves one
I don't know, but I bet it involves on
I don't know, but I bet it involves o
I don't know, but I bet it involves
I don't know, but I bet it involves
I don't know, but I bet it involve
I don't know, but I bet it involv
I don't know, but I bet it invol
I don't know, but I bet it invo
I don't know, but I bet it inv
I don't know, but I bet it in
I don't know, but I bet it i
I don't know, but I bet it
I don't know, but I bet it
I don't know, but I bet i
I don't know, but I bet
I don't know, but I bet
I don't know, but I be
I don't know, but I b
I don't know, but I
I don't know, but I
I don't know, but
I don't know, but
I don't know, bu
I don't know, b
I don't know,
I don't know,
I don't know
I don't kno
I don't kn
I don't k
I don't
I don't
I don'
I don
I do
I d
I
I
nice spoiler advert: did you wrote it line-by-line or it's a plugin?
In article <tnhua3$3bf70$3@dont-email.me>,
Richard Heathfield <rjh@cpax.org.uk> wrote:
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
I don't know, but I bet it involves one of these:
Indeed it does, but how do you use it?
This is probably well-known.
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
-- Richard
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
I don't know, but I bet it involves one of these:
In article <tnhua3$3bf70$3...@dont-email.me>,With affection.
Richard Heathfield <r...@cpax.org.uk> wrote:
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
I don't know, but I bet it involves one of these:Indeed it does, but how do you use it?
-- Richard
Indeed it does, but how do you use it?
On 12/16/2022 5:45 AM, Richard Tobin wrote:
This is probably well-known.
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
-- Richard
I wrote a similar puzzle for this group in 2005 entitled "Moe's
Game":
Moe has always been interested in games. Several years ago, Moe
invented a simple two-player word game. His game is played using
nine tiles. Each tile is labeled with a single letter of the
alphabet. The letters on the tiles are those in the phrase
"REMIND YOU", which helps "remind you" which letters to use. The
objective of the game is to collect the tiles necessary to spell
out any one of eight three-letter words. There are many
three-words that can be spelled using the letters, but Moe
selected the following eight words: END, ION, MUD, RIM, ROD, RYE,
and of course YOU and MOE (since Moe plays the game against you).
The game play is straight forward. The tiles are placed face-up
in a pile. The players then take turns removing one of the tiles
from the pile. The first player to collect the tiles necessary to
spell one of the eight words, wins. Sometimes Moe plays first,
and sometimes he lets his opponent play first. Although the game
occasionally ends in a draw (with neither player spelling one of
the words), Moe has never lost a game.
What is Moe's playing strategy?
On 16/12/2022 5:56 pm, Carl G. wrote:
On 12/16/2022 5:45 AM, Richard Tobin wrote:
This is probably well-known.
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
-- Richard
I wrote a similar puzzle for this group in 2005 entitled "Moe's Game":
Moe has always been interested in games. Several years ago, Moe invented a simple two-player word
game. His game is played using nine tiles. Each tile is labeled with a single letter of the
alphabet. The letters on the tiles are those in the phrase "REMIND YOU", which helps "remind you"
which letters to use. The objective of the game is to collect the tiles necessary to spell out any
one of eight three-letter words. There are many three-words that can be spelled using the letters,
but Moe selected the following eight words: END, ION, MUD, RIM, ROD, RYE, and of course YOU and
MOE (since Moe plays the game against you). The game play is straight forward. The tiles are
placed face-up in a pile. The players then take turns removing one of the tiles from the pile. The
first player to collect the tiles necessary to spell one of the eight words, wins. Sometimes Moe
plays first, and sometimes he lets his opponent play first. Although the game occasionally ends in
a draw (with neither player spelling one of the words), Moe has never lost a game.
What is Moe's playing strategy?
RYE
ION
MUD
As player 1, pick O, giving you an option on four lines.
Example: o (lower case for P1)
As player 2, pick R E M or D (a corner) for an option on two lines.
Example: (upper case for P1)
R
o
As player 1, pick a corner a single rook move away from Player 2's move (or possibly any corner; I
didn't think it through).
Example:
R
o
m
Player 2 must block:
R E
o
m
Player 1 must block:
RyE
o
m
Player 2 must block:
RyE
o
mU
Player 1's best bet is to block the third column and hope for P2 stupidity:
RyE
on
mU
Player 2 must block:
RyE
Ion
mU
and P1's move is forced.
Effectively a forced draw if neither side throws it away.
In numbers:
2 7 6
9 5 1
4 3 8
P1 picks 5.
P2 picks an even number x.
P1 picks an even number y such that x+y <> 10 (or possibly any even number - I didn't think it all
the way through).
P2 picks 10-y.
and now it's all blocking until P1's fourth move, where he has a theoretical winning line remaining
if his opponent is prepared to connive at his own destruction by failing to block it.
The key observation :
a)Â Every row/column/diagonal adds to 15 (clearly - it's the most
famous magic square)
b)Â Less obviously, EVERY combination of 3 numbers totalling 15
appears as a row/column/diagonal. That's not a requirement for a
magic square, but checking by hand, it applies in this square.
b) Less obviously, EVERY combination of 3 numbers totalling 15 appears
as a row/column/diagonal.
In article <3EmdnQFht6A0bgH-nZ2dnZfqn_qdnZ2d@brightview.co.uk>,
Mike Terry <news.dead.person.stones@darjeeling.plus.com> wrote:
b) Less obviously, EVERY combination of 3 numbers totalling 15 appears
as a row/column/diagonal.
I am sure that Richard H, as a Killer Sudoku player, would have
noticed this!
Hmm, a simple variation:
 Two players take it in turns to choose an integer between 1 and 9
 that has not already been chosen. The first player to acquire
 numbers totalling 15 wins.
(Very easy first player win)
This is probably well-known.
Two players take it in turns to choose an integer between 1 and 9
that has not already been chosen. The first player with three
numbers totalling 15 wins.
What is the optimal strategy for each player?
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