AOH :: PUZZLE09.FAQ
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Article 3073 of news.answers:
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Path: news.UVic.CA!ubc-cs!destroyer!uunet!questrel!chris
From: uunet!questrel!chris (Chris Cole)
Subject: rec.puzzles FAQ, part 9 of 15
Message-ID: <puzzles-faq-9_717034101@questrel.com>
Followup-To: rec.puzzles
Summary: This posting contains a list of
Frequently Asked Questions (and their answers).
It should be read by anyone who wishes to
post to the rec.puzzles newsgroup.
Sender: chris@questrel.com (Chris Cole)
Reply-To: uunet!questrel!faql-comment
Organization: Questrel, Inc.
References: <puzzles-faq-1_717034101@questrel.com>
Date: Mon, 21 Sep 1992 00:09:26 GMT
Approved: news-answers-request@MIT.Edu
Expires: Sat, 3 Apr 1993 00:08:21 GMT
Lines: 1553
Archive-name: puzzles-faq/part09
Last-modified: 1992/09/20
Version: 3
s Sunday School
ss liner
ss saints
ss ship
ss steamship
st good man
st hush
st little way
st paragon
st road
st saint
st silence
st stone
st street
st stumped
st thoroughfare
st way
st weight
stag speculator
sten gun
stet don't change it
stir prison
stop traffic signal
sts saints
sty filthy place
stye eyesore
su Soviet Union
sub U-boat
sub stand-in
sub substitute
sub warship
supra over
sure certain
sw Cornwall
sw Devon
sw bridge opponents
sw quarter
sw south-west
swift screecher
swiss roll jammed cylinder
sx Essex
t Thailand
t Tuesday
t bandage
t bar
t bone
t cart
t cloth
t cross
t crossed
t half dry
t hundred and sixty
t hundred and sixty thousand
t junction
t model +
t peg
t perfect letter
t plate
t rail
t shirt
t short time
t square
t tau
t te
t tea
t tee
t tesla
t the
t time
t ton(ne)
t tritium
ta Territorial Army
ta army
ta cheers
ta reserves
ta soldiers
ta terriers
ta territorials
ta thank you
ta thanks
ta volunteers
tab label
tace silence
tag label
tan beat
tan brown
tan maths function
tar able seaman
tar art nouveau
tar sailor/salt/seaman
tata Tosti's song
tata goodbye
tate gallery
tau cross
tay river
tb torpedo boat
td medal
te Lawrence
te note
tea leaves
tec detective
ted Edward
ted Heath
tee peg
teen old injury
tees river
tell archer
temp secretary
ten PM's address
tene old injury
tent wine
ter three (triple)
ter thrice
test educational journal
test examination
test match
teth Hebrew letter
the article
the articles - English
ti note
tic note
tic spasm
tic twitching
tier row
time father
times daily
timon misanthrope
tin can
tin cash
tin money
tin vessel
tiny small
tion empty container
tit bird
tit inferior horse
tit poor horse
tnt big banger
tnt explosive
tod fox
todo commotion
toe extremity
toe member
tom big bell
tom cat
tome book
ton fashion
ton hundred
ton large amount
ton weight
tonne weight
tor hell
tor hill
tor mountain
tor point
tor prominence
tory Conservative
tory party
tory politician
tp teepee
tr Turkey
tr transaction
tr translation
tram transport
tree actor
tres very (Fr.)
tri three (triple)
tri thrice
troy ancient city
troy old city
try attempt
try essay
ts teas
ts tees
tt abstaining
tt dry
tt on the wagon
tt race
tt teas
tt tees
tt teetotal
tt teetotaller
tt thank you
tu tradesmen
tuck friar
twelve eec
two company
u Conservative
u Uruguay
u Utah
u about turn
u acceptable
u bend
u boat
u educational establishment
u ewe
u film
u for all to see
u high class
u on view to all
u posh
u socially acceptable
u suitable for children
u superior
u trap
u tube
u turn
u union/Unionist
u universal
u university
u upper class
u uppish
u upsilon
u uranium
u yew
u you
uc you see
uk United Kingdom
uk this country
uk this island
ule rubber
ult last month
um doubt
um hesitation
un United Nations
un international
un number one (Fr.)
un one
un one (dialect)
un peacekeepers
una number one (Ital.)
unco very (Scot.)
une number one (Fr.)
uno international organisation
uno number one (Ital.)
up at university
up excited
up in court
up mounted
up riding
up superior
uq you queue
ur ancient city
ur hesitation
ur old city
ur primitive
ur you are
ure river
uru Uruguay
us America
us American
us as above
us ewes
us no good
us transatlantic
us undersecretary
us use
us useless
us yews
us you and me
usa America
use application
use custom
use employ(ment)
use practice
use practise
ussr Soviet Union
ut note
ute half minute
uu ewes
uu use
uu yews
ux wife
v Vatican
v against
v agent
v bomb
v day
v five
v look
v neck
v neckline
v notch
v opposing
v see
v sign
v vanadium
v vee
v velocity
v verb
v verse
v versus
v very
v victory
v vide
v volt
v volume
v win
va Virginia
vad nurse
vale farewell
vale goodbye
vat tax
vau Hebrew letter
vb verb
ve victory
ver rev up
very light
vet surgeon
vg for example
vi half dozen
vi six
via old way
vid see
vid tanner/sixpence
vide look
vide see
vin French wine
vip big noise
vip tanner/sixpence
vir man/Roman
vis viscount
vj victory
vo left hand
vol book
vol volume
vy various years
w Wednesday
w Welsh
w William
w bridge players
w direction
w point
w quarter
w tungsten
w watt
w weak
w west(ern)
w whole numbers
w wicket
w width
w wife
w woman
ward disadvantage (drawback)
washington young feller
we partnership
we you and I
wee little
wee minor
wee small
who doctor
wi Mayfair
wi West Indies
wi Westminster
winner fabulous tortoise
wise youth leaders
wist knew (old word)
women monstrous regiment
woof bark
wt small weight
wt weight
x Christ
x PM's address
x Xmas
x across
x body
x chi
x chromosome
x cross
x draw
x ex,Exe
x film
x illiterate's signature
x kiss
x particle
x ray
x sign of love
x sign of the times
x spot marked
x ten
x ten thousand
x thousand
x times
x unknown
x vitamin
x vote
x wrong sign
x xi
xc ninety
xi eleven
xi side
xi team
xl excel
xv side
xv team
y alloy
y chromosome
y level
y measure
y moth
y one hundred and fifty
y one hundred and fifty thousand
y track
y unknown
y why
y yard
y year
y yen
y young
y yttrium
yard detectives
yd measure
ye the (old word)
ye you (old word)
yea agreement
yew tree
yr year
yr your
ys wise
ys youth leaders
yt that (old word)
yu jade
yule you will, say
yy wise
z Zambia
z bar
z bend
z cedilla
z final letter
z integers
z izzard
z last character
z last letter
z omega
z seven
z seven thousand
z sound of sleep
z zed
z zee
z zero
z zeta
zo cross *
zr Zaire
zz (sound of) snoring
----------------------------------------------------------------------
--
Ross Beresford, | Email (trusted): rberesfo@cix.compulink.co.uk
10 Wagtail Close, | (work): ross@siesoft.co.uk
Twyford, Reading, | (under test): ross@dickens.demon.co.uk
RG10 9ED, UK |
==> games/crosswords/cryptic/double.p <==
Each clue has two solutions, one for each diagram; one of the answers
to 1ac. determines which solutions are for which diagram.
All solutions are in Chamber's and Webster's Third except for one solution
of each of 1dn, 3dn and 4dn, which can be found in Webster's 2nd. edition.
#######################################################################
#1 |2 | | |3 |4 |5 #1 |2 | | |3 |4 |5 #
# | | | | | | # | | | | | | #
#----+----###########----#----#----#----+----###########----#----#----#
#6 | |7 | | # # #6 | |7 | | # # #
# | | | | # # # | | | | # # #
#----#----#----######----#----#----#----#----#----######----#----#----#
# # # #8 | | | # # # #8 | | | #
# # # # | | | # # # # | | | #
#----#----#----######----#----#----#----#----#----######----#----#----#
#9 | | | # # # #9 | | | # # # #
# | | | # # # # | | | # # # #
#----#----#----######----#----#----#----#----#----######----#----#----#
# # #10 | | | | # # #10 | | | | #
# # # | | | | # # # | | | | #
#----#----#----###########----+----#----#----#----###########----+----#
#11 | | | | | | #11 | | | | | | #
# | | | | | | # | | | | | | #
#######################################################################
Ac.
1. What can have distinctive looking heads spaced about more prominently
right. (7)
6. Vermin that can overrun fish and t'English tor perhaps. (5)
8. Old testament reversal - Adam's conclusion, start of sin.
Felines initially with everything there. (4)
9. Black initiated cut, oozed out naturally. (4)
10. For instance, 11 with spleen dropping I count? (5)
11. Provoked explosion of grenade. (7)
Dn.
1. Some of club taking part in theatrical function, for the equivalent
of a fraction of a pound. (6)
2. Close-in light meter in one formation originally treated as limestone. (6)
3. Xingu River hombres having symmetrical shape. (5)
4. About sex-appeal measure - what waitresses should be? (6)
5. Old penny, least damaged, was preserved. (6)
7. IRA to harm ruling Englishman; extremes could be belonging to group. (5)
==> games/crosswords/cryptic/double.s <==
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|r e d c a p s|d e x t r a l|
+ + +-+-+ + + + + +-+-+ + + +
|o t t e r|o|a|r o a c h|s|a|
+ + + +-+ + + + + + +-+ + + +
|u|a|h|f a l l|a|z|m|t o m s|
+ + + +-+ + + + + + +-+ + + +
|b l e d|r|i|t|c o o n|m|i|t|
+ + + +-+ + + + + + +-+ + + +
|l|o|i r a t e|m|o|n o b l e|
+ + + +-+-+ + + + + +-+-+ + +
|e n r a g e d|a n g e r e d|
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Notes.
Left grid: Ac. 1. R + spaced (anag). 6. T'E tor (anag). 8. F-all. 9. B-led.
10. I-rate. Dn. 1. Ro-ub-le. 2. T.A.L. in one (anag). 4. it in pole.
5. anag of D+least. 7. anag of initial letters.
Right grid: Ac. 1. D-extra-L. 6. 3 mngs. 8. OT (rev) + m-s.
9. initial letters. 10. No.-b(i)le. Dn. Dra-c-ma. 2. Zoo(m) in one (anag).
3. hidden. 4. SA (rev) + mile. 5. anag of D+least. 7. anag of final letters.
--------------------------------------------------------------------
How I built it: it was hard!
Basically, I started with a couple of word pairs which were easy to clue
(e.g. enraged/angered - same meaning and anagrams of each other)
and built a grid around them, trying to ensure corresponding words
had something in common, either in meaning (their, among) or structure,
(EtalON, EOzooN) and making sure that there was at least one word
which could be used to distinguish the two grids (dextral).
The clues were built in one of two ways:
either the words had a common definition, and so a subsidiary indication
which could refer to either was needed; or it was necessary to define each
word in such a way that it was a subsidiary definition for all or part
of the corresponding word, and deal with any remaining parts as before.
I think the single hardest part was finding a definition of "interferometer"
which could also be interpreted as "zoo" or "ozo".
Roy
rt@ukc.ac.uk
==> games/crosswords/cryptic/intro.p <==
What are the rules for cluing cryptic crosswords?
==> games/crosswords/cryptic/intro.s <==
This is a brief set of instructions for solving cryptic crossword puzzles
for those of you who are intrigued by these puzzles, but haven't known how
to begin solving them. For a more complete introduction, send a
self-addressed, stamped envelope to The Atlantic Puzzler, 745 Boylston
Street, Boston, Mass. 02116.
The characteristic common to all cryptic crossword puzzles is the format of
the clues. Each clue is a miniature word puzzle consisting of a straight
definition of the answer and a cryptic definition of the answer. For
example,
Axle is poorly splined (7)
yields SPINDLE. Axle is the straight definition. The cryptic definition
(poorly splined) indicates an anagram of "splined". The number in
parentheses is the number of letters in the answer. Punctuation and
capitalization may be ignored in interpreting the clues.
There are only eight categories of clues, as follows:
1. Anagram
An anagram is a word formed by mixing up the letters of another word. An
anagram clue is indicated by some word that means "mixed up", for
example, out, crazy, bizarre, insane, etc. One or more words may
contribute to the anagram. For example:
Tim goes insane from selfishness (7)
for EGOTISM (anagram of "Tim goes")
2. Double Definition
A double definition is simply two definitions of the word. Most two-word
clues are double definitions. For example:
Release without charge (4)
for FREE
3. Container
A container clue indicates that something is to be put in (or wrapped
around) something else. A container is indicated by phrases such as
eaten by, contains, in, gobbles, etc. For example:
In Missouri, consumed by fear (7)
for AMONGST (MO = Missouri in ANGST = fear)
4. Hidden Word
A hidden word is a word embedded in another word or words. It is
indicated by phrases such as spot in, hides, at the heart of, covers,
etc. For example:
Worn spot in paper at typo (5)
for RATTY (find ratty in "paper at typo")
5. Reversal
A reversal is a definition of a word with the letters reversed. It is
indicated by words such as back, reversed, up (for down clues), leftward
(for across clues), etc. For example:
Egad! Ray entirely reversed the lot of cloth (7)
for YARDAGE ("Egad! Ray" reversed)
6. Homophone
A homophone definition is a definition of a word that sounds the same as
the answer, but is spelled differently. A homophone is indicated by
words such as in audience, I hear, mouthed, verbally, etc. For example:
Regrets prank, I hear (4)
for RUES (the homophone is RUSE = prank)
7. Charade
In a charade, the pieces of the word are "spelled" out in order. There
are no auxiliary words that indicate a charade. For example:
Excite a jerk extremist (7)
for FANATIC (FAN = excite, A, TIC = jerk)
8. Deletion
A deletion is a clue where you are instructed to remove a part of some
word to make another word. For example,
Times with poor wages (4)
for AGES (with-poor WAGES, where with is abbreviated by W)
Often the clue types are combined. Some common examples are 1) hidden word
reversals where the answer is found backwards embedded in other words, and
2) containers or charades where the parts are anagrams. For example:
Car shops have broken gear immersed in gasoline. (7)
for GARAGES (RAGE = gear anagram in GAS = gasoline)
All manner of common abbreviations, acronyms, and other symbology such as
roman numerals are allowed. For example:
c one hundred, cup, or centigrade
vi six
h hot
s small
ca california
Two punctuation marks at the end of the clue have been reserved for special
meaning. A question mark (?) indicates that the straight clue is not
entirely straight (usually a pun). For example:
I tie down mascara holder soundly? (7)
for EYELASH (homophone of "I lash", mascara holder is a punning
definition of EYELASH)
An exclamation point (!) indicates that some part (usually all) of the clue
overlaps. For example, the straight definition may also be the anagram
indicator. Here is an example that entirely overlaps:
A moped also has these! (6)
for PEDALS (hidden word)
Here, the entire clue indicates the hidden word, but the entire clue is
also a straight definition of the answer.
Give it a try! Cryptic crossword puzzles are a lot of fun.
-- Steve Koehler
ucsd.edu!telesoft!koehler
telesoft!koehler@ucsd.edu
koehler@telesoft.com
==> games/go-moku.p <==
For a game of k in a row on an n x n board, for what values of k and n is
there a win? Is (the largest such) k eventually constant or does it increase
with n?
==> games/go-moku.s <==
Berlekamp, Conway, and Guy's _Winning_Ways_ reports proof that the
maximum k is between 4 and 7 inclusive, and it appears to be 5 or 6.
They report:
. 4-in-a-row is a draw on a 5x5 board (C. Y. Lee), but not on a 4x30
board (C. Lustenberger).
. N-in-a-row is shown to be a draw on a NxN board for N>4, using a
general pairing technique devised by A. W. Hales and R. I. Jewett.
. 9-in-a-row is a draw even on an infinite board, a 1954 result of H. O.
Pollak and C. E. Shannon.
. More recently, the pseudonymous group T. G. L. Zetters showed that
8-in-a-row is a draw on an infinite board, and have made some
progress on showing infinite 7-in-a-row to be a draw.
Go-moku is 5-in-a-row played on a 19x19 go board. It is apparently a
win for the first player, and so the Japanese have introduced several
'handicaps' for the first player (e.g., he must win with _exactly_
five: 6-in-a-row doesn't count), but apparently the game is still a win
for the first player. None of these apparent results have been
proven.
==> games/hi-q.p <==
What is the quickest solution of the game Hi-Q (also called Solitair)?
For those of you who aren't sure what the game looks like:
32 movable pegs ("+") are arranged on the following board such that
only the middle position is empty ("-"). Just to be complete: the board
consists of only these 33 positions.
1 2 3 4 5 6 7
1 + + +
2 + + +
3 + + + + + + +
4 + + + - + + +
5 + + + + + + +
6 + + +
7 + + +
A piece moves on this board by jumping over one of its immediate
neighboor (horizontally or vertically) into an empty space opposite.
The peg that was jumped over, is hit and removed from the board. A
move can contain multiple hits if you use the same peg to make the
hits.
You have to end with one peg exactly in the middle position (44).
==> games/hi-q.s <==
1: 46*44
2: 65*45
3: 57*55
4: 54*56
5: 52*54
6: 73*53
7: 43*63
8: 75*73*53
9: 35*55
10: 15*35
11: 23*43*63*65*45*25
12: 37*57*55*53
13: 31*33
14: 34*32
15: 51*31*33
16: 13*15*35
17: 36*34*32*52*54*34
18: 24*44
Found by Ernest Bergholt in 1912 and was proved to be minimal by John Beasley
in 1964.
References
The Ins and Outs of Peg Solitaire
John D Beasley
Oxford U press, 1985
ISBN 0-19-853203-2
Winning Ways, Vol. 2, Ch. 23
Berlekamp, E.R.
Academic Press, 1982
ISBN 01-12-091102-7
==> games/jeopardy.p <==
What are the highest, lowest, and most different scores contestants
can achieve during a single game of Jeopardy?
==> games/jeopardy.s <==
highest: $283,200.00, lowest: -$29,000.00, biggest difference: $309,700.00
(1) Our theoretical contestant has an itchy trigger finger, and rings in with
an answer before either of his/her opponents.
(2) The daily doubles (1 in the Jeopardy! round, 2 in the Double Jeopardy!
round) all appear under an answer in the $100 or $200 rows.
(3) All answers given by our contestant are (will be?) correct.
Therefore:
Round 1 (Jeopardy!): Max. score per category: $1500.
For 6 categories - $100 for the DD, that's $8900.
Our hero bets the farm and wins - score: $17,800.
Round 2 (Double Jeopardy!):
Max. score per category: $3000.
Assume that the DDs are found last, in order.
For 6 categories - $400 for both DDs, that's $17,600.
Added to his/her winnings in Round 1, that's $35,400.
After the 1st DD, where the whole thing is wagered,
the contestant's score is $70,800. Then the whole
amount is wagered again, yielding a total of $141,600.
Round 3 (Final Jeopardy!):
Our (very greedy! :) hero now bets the whole thing, to
see just how much s/he can actually win. Assuming that
his/her answer is right, the final amount would be
$283,200.
But the contestant can only take home $100,000; the rest is donated to
charity.
To calculate the lowest possible socre:
-1500 x 6 = -9000 + 100 = -8900.
On the Daily Double that appears in the 100 slot, you bet the maximum
allowed, 500, and lose. So after the first round, you are at -9400.
-3000 x 6 = -18000 + 400 = -17600
On the two Daily Doubles in the 200 slots, bet the maximum allowed, 1000. So
after the second round you are at -9400 + -19600 = -29000. This is the
lowest score you can achieve in Jeopardy before the Final Jeopardy round.
The caveat here is that you *must* be the person sitting in the left-most
seat (either a returning champion or the luckier of the three people who
come in after a five-time champion "retires") at the beginning of the game,
because otherwise you will not have control of the board when the first
Daily Double comes along.
==> games/knight.tour.p <==
For what board sizes is a knight's tour possible?
==> games/knight.tour.s <==
A tour exists for boards of size 1x1, 3x4, 3xN with N >= 7, 4xN with N >= 5,
and MxN with N >= M >= 5. In other words, for all rectangles except 1xN
(excluding the trivial 1x1), 2xN, 3x3, 3x5, 3x6, 4x4.
With the exception of 3x8 and 4xN, any even-sized board which allows a tour
will also allow a closed (reentrant) tour.
On an odd-sided board, there is one more square of one color than
of the other. Every time a knight moves, it moves to a square of
the other color than the one it is on. Therefore, on an odd-sided
board, it must end the last move but one of the complete, reentrant
tour on a square of the same color as that on which it started.
It is then impossible to make the last move, for that move would end
on a square of the same color as it begins on.
Here is a solution for the 7x7 board (which is not reentrant).
------------------------------------
| 17 | 6 | 33 | 42 | 15 | 4 | 25 |
------------------------------------
| 32 | 47 | 16 | 5 | 26 | 35 | 14 |
------------------------------------
| 7 | 18 | 43 | 34 | 41 | 24 | 3 |
------------------------------------
| 46 | 31 | 48 | 27 | 44 | 13 | 36 |
------------------------------------
| 19 | 8 | 45 | 40 | 49 | 2 | 23 |
------------------------------------
| 30 | 39 | 10 | 21 | 28 | 37 | 12 |
------------------------------------
| 9 | 20 | 29 | 38 | 11 | 22 | 1 |
------------------------------------
Here is a solution for the 5x5 board (which is not reentrant).
--------------------------
| 5 | 10 | 15 | 20 | 3 |
--------------------------
| 16 | 21 | 4 | 9 | 14 |
--------------------------
| 11 | 6 | 25 | 2 | 19 |
--------------------------
| 22 | 17 | 8 | 13 | 24 |
--------------------------
| 7 | 12 | 23 | 18 | 1 |
--------------------------
Here is a reentrant 2x4x4 tour:
0 11 16 3 15 4 1 22
19 26 9 24 8 23 14 27
10 5 30 17 31 12 21 2
29 18 25 6 20 7 28 13
A reentrant 4x4x4 tour can be constructed by splicing two copies.
It shouldn't be much more work now to completely solve the problem of which 3D
rectangular boards allow tours.
==> games/nim.p <==
Place 10 piles of 10 $1 bills in a row. A valid move is to reduce
the last i>0 piles by the same amount j>0 for some i and j; a pile
reduced to nothing is considered to have been removed. The loser
is the player who picks up the last dollar, and they must forfeit
half of what they picked up to the winner.
1) Who is the winner in Waldo Nim, the first or the second player?
2) How much more money than the loser can the winner obtain with best
play on both parties?
==> games/nim.s <==
For the particular game described we only need to consider positions for
which the following condition holds for each pile:
(number of bills in pile k) + k >= (number of piles) + 1
A GOOD position is defined as one in which this condition holds,
with equality applying only to one pile P, and all piles following P
having the same number of bills as P.
( So the initial position is GOOD, the special pile being the first. )
I now claim that if I leave you a GOOD position, and you make any move,
I can move back to a GOOD position.
Suppose there are n piles and the special pile is numbered (n-p+1)
(so that the last p piles each contain p bills).
(1) You take p bills from p or more piles;
(a) If p = n, you have just taken the last bill and lost.
(b) Otherwise I reduce pile (n-p) (which is now the last) to 1 bill.
(2) You take p bills from r(<p) piles;
I take r bills from (p-r) piles.
(3) You take q(<p) bills from p or more piles;
I take (p-q) bills from q piles.
(4) You take q(<p) bills from r(<p) piles;
(a) q+r>p; I take (p-q) bills from (q+r-p) piles
(b) q+r<=p; I take (p-q) bills from (q+r) piles
Verifying that each of the resulting positions is GOOD is tedious
but straightforward. It is left as an exercise for the reader.
-- RobH
==> games/othello.p <==
How good are computers at Othello?
==> games/othello.s <==
The interesting game in which computers are undoubted masters of all they
survey is Othello, where Kai-Fu Lee's (CMU) program "Bill" is so good it can
only play itself to learn to get better. Bill has a fantastically
correct and efficient evaluation function, that recently has been further
improved by learning coefficients for additional terms made up of the
pair-wise combination of the four old terms. This improved the quality
of the play approximately as much as searching an extra two ply.
Bill is so good it can beat lots of players with no search at all. Its
6 or 7 ply search sweeps aside all opposition (though Kai-Fu says that some
very good players are now coming along in Japan, and he is not sure whether
Bill would beat them). One interesting question remaining in Othello is
the game theoretic value of the starting position. Bill's results seem
to indicate that the first player has an advantage. It appears that,
since Kai-Fu has published all his evaluation material, someone could
build an Othello machine, and produce a constructive proof (as was done
for Cubic) that it is a win for the first player.
==> games/risk.p <==
What are the odds when tossing dice in Risk?
==> games/risk.s <==
Attacker using 3 dice, Defender using 2:
Probability that Attacker wins 2 = 2323 / 7776
Probability that Attacker wins 1 = 3724 / 7776
Probability that Attacker wins 0 = 1729 / 7776
Attacker using 3 dice, Defender using 1:
Probability that Attacker wins 1 = 855 / 1296
Probability that Attacker wins 0 = 441 / 1296
Attacker using 2 dice, Defender using 2:
Probability that Attacker wins 2 = 225 / 1296
Probability that Attacker wins 1 = 630 / 1296
Probability that Attacker wins 0 = 441 / 1296
Attacker using 2 dice, Defender using 1:
Probability that Attacker wins 1 = 125 / 216
Probability that Attacker wins 0 = 91 / 216
Attacker using 1 dice, Defender using 2:
Probability that Attacker wins 1 = 90 / 216
Probability that Attacker wins 0 = 126 / 216
Attacker using 1 dice, Defender using 1:
Probability that Attacker wins 1 = 15 / 36
Probability that Attacker wins 0 = 21 / 36
==> games/rubiks.clock.p <==
How do you quickly solve Rubik's clock?
==> games/rubiks.clock.s <==
Solution to Rubik's Clock
The solution to Rubik's Clock is very simple and the clock can be
"worked" in 10-20 seconds once the solution is known.
In this description of how to solve the clock I will describe
the different clocks as if they were on a map (e.g. N,NE,E,SE,S,SW,W,NW);
this leaves the middle clock which I will just call M.
To work the Rubik's clock choose one side to start from; it does
not matter from which side you start. Your initial goal
will be to align the N,S,E,W and M clocks. Use the following algorithm
to do this:
[1] Start with all buttons in the OUT position.
[2] Choose a N,S,E,W clock that does not already have the
same time as M (i.e. not aligned with M).
[3] Push in the closest two buttons to the clock you chose in [2].
[4] Using the knobs that are farest away from the clock you chose in
[2] rotate the knob until M and the clock you chose are aligned.
The time on the clocks at this point does not matter.
[5] Go back to [1] until N,S,E,W and M are in alignment.
[6] At this point N,S,E,W and M should all have the same time.
Make sure all buttons are out and rotate any knob
until N,S,E,W and M are pointing to 12 oclock.
Now turn the puzzle over and repeat steps [1]-[6] for this side. DO NOT
turn any knobs other than the ones described in [1]-[6]. If you have
done this correctly then on both sides of the puzzle N,S,E,W and M will
all be pointing to 12.
Now to align NE,SE,SW,NW. To finish the puzzle you only need to work from
one side. Choose a side and use the following algorithm to align the
corners:
[1] Start with all buttons OUT on the side you're working from.
[2] Choose a corner that is not aligned.
[3] Press the button closest to that corner in.
[4] Using any knob except for that corner's knob rotate all the
clocks until they are in line with the corner clock.
(Here "all the clocks" means N,S,E,W,M and any other clock
that you have already aligned)
There is no need at this point to return the clocks to 12
although if it is less confusing you can. Remember to
return all buttons to their up position before you do so.
[5] Return to [1] until all clocks are aligned.
[6] With all buttons up rotate all the clocks to 12.
==> games/rubiks.cube.p <==
What is known about bounds on solving Rubik's cube?
==> games/rubiks.cube.s <==
The "official" world record was set by Minh Thai at the 1982 World
Championships in Budapest Hungary, with a time of 22.95 seconds.
Keep in mind mathematicians provided standardized dislocation patterns
for the cubes to be randomized as much as possible.
The fastest cube solvers from 19 different countries had 3 attempts each
to solve the cube as quickly as possible. Minh and several others have
unofficially solved the cube in times between 16 and 19 seconds.
However, Minh averages around 25 to 26 seconds after 10 trials, and by
best average of ten trials is about 27 seconds (although it is usually
higher).
Consider that in the World Championships 19 of the world's fastest cube
solvers each solved the cube 3 times and no one solved the cube in less
than 20 seconds...
God's algorithm is the name given to an as yet (as far as I know)
undiscovered method to solve the rubik's cube in the least number of moves;
as apposed to using 'canned' moves.
The known lower bound is 18 moves. This is established by looking at things
backwards: suppose we can solve a position in N moves. Then by running the
solution backwards, we can also go from the solved position to the position
we started with in N moves. Now we count how many sequences of N moves there
are from the starting position, making certain that we don't turn the same
face twice in a row:
N=0: 1 (empty) sequence;
N=1: 18 sequences (6 faces can be turned, each in 3 different ways)
N=2: 18*15 sequences (take any sequence of length 1, then turn any of the
five faces which is not the last face turned, in any of 3 different
ways);
N=3: 18*15*15 sequences (take any sequence of length 2, then turn any of
the five faces which is not the last face turned, in any of 3
different ways);
:
:
N=i: 18*15^(i-1) sequences.
So there are only 1 + 18 + 18*15 + 18*15^2 + ... + 18*15^(n-1) sequences of
moves of length n or less. This sequence sums to (18/14)*(15^n - 1) + 1.
Trying particular values of n, we find that there are about 8.4 * 10^18
sequences of length 16 or less, and about 1.3 times 10^20 sequences of
length 17 or less.
Since there are 2^10 * 3^7 * 8! * 12!, or about 4.3 * 10^19, possible
positions of the cube, we see that there simply aren't enough sequences of
length 16 or less to reach every position from the starting position. So not
every position can be solved in 16 or less moves - i.e. some positions
require at least 17 moves.
This can be improved to 18 moves by being a bit more careful about counting
sequences which produce the same position. To do this, note that if you turn
one face and then turn the opposite face, you get exactly the same result as
if you'd done the two moves in the opposite order. When counting the number
of essentially different sequences of N moves, therefore, we can split into
two cases:
(a) Last two moves were not of opposite faces. All such sequences can be
obtained by taking a sequence of length N-1, choosing one of the 4 faces
which is neither the face which was last turned nor the face opposite
it, and choosing one of 3 possible ways to turn it. (If N=1, so that the
sequence of length N-1 is empty and doesn't have a last move, we can
choose any of the 6 faces.)
(b) Last two moves were of opposite faces. All such sequences can be
obtained by taking a sequence of length N-2, choosing one of the 2
opposite face pairs that doesn't include the last face turned, and
turning each of the two faces in this pair (3*3 possibilities for how it
was turned). (If N=2, so that the sequence of length N-2 is empty and
doesn't have a last move, we can choose any of the 3 opposite face
pairs.)
This gives us a recurrence relation for the number X_N of sequences of
length N:
N=0: X_0 = 1 (the empty sequence)
N=1: X_1 = 18 * X_0 = 18
N=2: X_2 = 12 * X_1 + 27 * X_0 = 243
N=3: X_3 = 12 * X_2 + 18 * X_1 = 3240
:
:
N=i: X_i = 12 * X_(i-1) + 18 * X_(i-2)
If you do the calculations, you find that X_0 + X_1 + X_2 + ... + X_17 is
about 2.0 * 10^19. So there are fewer essentially different sequences of
moves of length 17 or less than there are positions of the cube, and so some
positions require at least 18 moves.
The upper bound of 50 moves is I believe due to Morwen Thistlethwaite, who
developed a technique to solve the cube in a maximum of 50 moves. It
involved a descent through a chain of subgroups of the full cube group,
starting with the full cube group and ending with the trivial subgroup (i.e.
the one containing the solved position only). Each stage involves a careful
examination of the cube, essentially to work out which coset of the target
subgroup it is in, followed by a table look-up to find a sequence to put it
into that subgroup. Needless to say, it was not a fast technique!
But it was fascinating to watch, because for the first three quarters or so
of the solution, you couldn't really see anything happening - i.e. the
position continued to appear random! If I remember correctly, one of the
final subgroups in the chain was the subgroup generated by all the double
twists of the faces - so near the end of the solution, you would suddenly
notice that each face only had two colours on it. A few moves more and the
solution was complete. Completely different from most cube solutions, in
which you gradually see order return to chaos: with Morwen's solution, the
order only re-appeared in the last 10-15 moves.
With God's algorithm, of course, I would expect this effect to be even more
pronounced: someone solving the cube with God's algorithm would probably
look very much like a film of someone scrambling the cube, run in reverse!
Finally, something I'd be curious to know in this context: consider the
position in which every cubelet is in the right position, all the corner
cubelets are in the correct orientation, and all the edge cubelets are
"flipped" (i.e. the only change from the solved position is that every edge
is flipped). What is the shortest sequence of moves known to get the cube
into this position, or equivalently to solve it from this position? (I know
of several sequences of 24 moves that do the trick.)
The reason I'm interested in this particular position: it is the unique
element of the centre of the cube group. As a consequence, I vaguely suspect
(I'd hardly like to call it a conjecture :-) it may lie "opposite" the
solved position in the cube graph - i.e. the graph with a vertex for each
position of the cube and edges connecting positions that can be transformed
into each other with a single move. If this is the case, then it is a good
candidate to require the maximum possible number of moves in God's
algorithm.
-- David Seal dseal@armltd.co.uk
To my knowledge, no one has ever demonstrated a specific cube position
that takes 15 moves to solve. Furthermore, the lower bound is known to
be greater than 15, due to a simple proof.
The way we know the lower bound is by working backwards counting how
many positions we can reach in a small number of moves from the solved
position. If this is less than 43,252,003,274,489,856,000 (the total
number of positions of Rubik's cube) then you need more than that
number of moves to reach the other positions of the cube. Therefore,
those positions will require more moves to solve.
The answer depends on what we consider a move. There are three common
definitions. The most restrictive is the QF metric, in which only a
quarter-turn of a face is allowed as a single move. More common is
the HF metric, in which a half-turn of a face is also counted as a
single move. The most generous is the HS metric, in which a quarter-
turn or half-turn of a central slice is also counted as a single move.
These metrics are sometimes called the 12-generator, 18-generator, and
27-generator metrics, respectively, for the number of primitive moves.
The definition does not affect which positions you can get to, or even
how you get there, only how many moves we count for it.
The answer is that even in the HS metric, the lower bound is 16,
because at most 17,508,850,688,971,332,784 positions can be reached
within 15 HS moves. In the HF metric, the lower bound is 18, because
at most 19,973,266,111,335,481,264 positions can be reached within 17
HF moves. And in the QT metric, the lower bound is 21, because at
most 39,812,499,178,877,773,072 positions can be reached within 20 QT
moves.
-- jjfink@skcla.monsanto.com writes:
Lately in this conference I've noted several messages related to Rubik's
Cube and Square 1. I've been an avid cube fanatic since 1981 and I've
been gathering cube information since.
Around Feb. 1990 I started to produce the Domain of the Cube Newsletter,
which focuses on Rubik's Cube and all the cube variants produced to
date. I include notes on unproduced prototype cubes which don't even
exist, patent information, cube history (and prehistory), computer
simulations of puzzles, etc. I'm up to the 4th issue.
Anyways, if you're interested in other puzzles of the scramble by
rotation type you may be interested in DOTC. It's available free to
anyone interested. I am especially interested in contributing articles
for the newsletter, e.g. ideas for new variants, God's Algorithm.
Anyone ever write a Magic Dodecahedron simulation for a computer? Anyone
understand Morwen Thistlethwaite's 50 move solution to Rubik's Cube? I'd
love to hear from you.
Drop me a SASE (say empire size) if you're interested in DOTC or if you
would like to exchange notes on Rubik's Cube, Square 1 etc.
I'm also interested in exchanging puzzle simulations, e.g. Rubik's Cube,
Twisty Torus, NxNxN Simulations, etc, for Amiga and IBM computers. I've
written several Rubik's Cube solving programs, and I'm trying to make
the definitive puzzle solving engine. I'm also interested in AI programs
for Rubik's Cube and the like.
Ideal Toy put out the Rubik's Cube Newsletter, starting with
issue #1 on May 1982. There were 4 issues in all, and I'm missing
#3.
I have: #1, May 1982
#2, Aug 1982
#3, Aug 1983
I am willing to trade photocopies with anyone to obtain #3.
There was another sort of magazine, published in several languages
called Rubik's Logic and Fantasy in space. I believe there were 8
issues in all. Unfortunately I don't have any of these! I'm willing
to buy these off anyone interesting in selling. I would like to get the
originals if at all possible...
I'm also interested in buying any books on the cube or related puzzles.
In particular I am _very_ interested in obtaining the following:
Cube Games Don Taylor, Leanne Rylands
Official Solution to Alexander's Star Adam Alexander
The Amazing Pyraminx Dr. Ronald Turner-Smith
The Winning Solution Minh Thai
The Winning Solution to Rubik's Revenge Minh Thai
Simple Solutions to Cubic Puzzles James G. Nourse
I'm also interested in buying puzzles of the mechanical type.
I'm still missing the Pyraminx Star (basically a Pyraminx with more tips
on it), the Puck, and Hungarian Rings.
If anyone out here is a fellow collector I'd like to hear from you.
If you have a cube variant which you think is rare, or an idea for a
cube variant we could swap notes.
I'm in the middle of compiling an exhaustive library for computer
simulations of puzzles. This includes simulations of all Uwe Meffert's
puzzles which he prototyped but _never_ produced. In fact, I'm in the
middle of working on a Pyraminx Hexagon solver. What? Never heard of it?
Meffert did a lot of other puzzles which never were made.
I invented some new "scramble by rotation" puzzles myself. My favourite
creation is the Twisty Torus. It is a torus puzzle with segments (which
slide around 360 degrees) with multiple rings around the circumference.
The computer puzzle simulation library I'm forming will be described
in depth in DOTC #4 (The Domain of the Cube Newsletter). So if you
have any interesting computer puzzle programs please email me and
tell me all about them!
Also to the people interested in obtaining a subscription to DOTC,
who are outside of Canada (which it seems is just about all of you!)
please don't send U.S. or non-Canadian stamps (yeah, I know I said
Self-Addressed Stamped Envelope before). Instead send me an
international money order in Canadian funds for $6. I'll send you
the first 4 issues (issue #4 is almost finished).
Mark Longridge
Address: 259 Thornton Rd N, Oshawa Ontario Canada, L1J 6T2
Email: mark.longridge@canrem.com
One other thing, the six bucks is not for me to make any money. This
is only to cover the cost of producing it and mailing it. I'm
just trying to spread the word about DOTC and to encourage other
mechanical puzzle lovers to share their ideas, books, programs and
puzzles. Most of the programs I've written and/or collected are
shareware for C64, Amiga and IBM. I have source for all my programs
(all in C or Basic) and I am thinking of providing a disk with the
4th issue of DOTC. If the response is favourable I will continue
to provide disks with DOTC.
-- Mark Longridge <mark.longridge@canrem.com> writes:
It may interest people to know that in the latest issue of "Cubism For Fun" %
(# 28 that I just received yesterday) there is an article by Herbert Kociemba
from Darmstadt. He describes a program that solves the cube. He states that
until now he has found no configuration that required more than 21 turns to
solve.
He gives a 20 move manoeuvre to get at the "all edges flipped/
all corners twisted" position:
DF^2U'B^2R^2B^2R^2LB'D'FD^2FB^2UF'RLU^2F'
or in Varga's parlance:
dofitabiribirilobadafodifobitofarolotifa
Other things #28 contains are an analysis of Square 1, an article about
triangular tilings by Martin Gardner, and a number of articles about other
puzzles.
--
% CFF is a newsletter published by the Dutch Cubusts Club NKC.
Secretary:
Anneke Treep
Postbus 8295
6710 AG Ede
The Netherlands
Membership fee for 1992 is DFL 20 (about$ 11).
--
-- dik t. winter <dik@cwi.nl>
References:
E. C. Turner & K. F. Gold, "Rubik's Groups", American Mathematical Monthly,
vol. 92 (1985), pp. 617-629.
Cubelike Puzzles - What Are They and How Do You Solve Them?
J.A. Eidswick A.M.M. March, 1986
Rubik's Revenge: The Group Theoretical Solution
Mogens Esrom Larsen A.M.M. June-July, 1985
The Group of the Hungarian Magic Cube
Chris Rowley Proceedings of the First Western Austrialian
Conference on Algebra, 1982
Rubik's Cubic Compendium
Erno Rubik, Tamas Varga, et al
(Ed by David Singmaster)
Oxford University Press, 1987
(Some chapters on mathematics of the cube.)
David Singmaster, _Notes on Rubik's `Magic Cube'_
"Winning Ways"
by
Berlekamp, Elwyn R.
Conway, John H.
Guy, Richard K.
Volume two, pages 760-768, 808, 809
==> games/rubiks.magic.p <==
How do you solve Rubik's Magic?
==> games/rubiks.magic.s <==
The solution is in a 3x3 grid with a corner missing.
+---+---+---+ +---+---+---+---+
| 3 | 5 | 7 | | 1 | 3 | 5 | 7 |
+---+---+---+ +---+---+---+---+
| 1 | 6 | 8 | | 2 | 4 | 6 | 8 |
+---+---+---+ +---+---+---+---+
| 2 | 4 | Original Shape
+---+---+
To get the 2x4 "standard" shape into this shape, follow this:
1. Lie it flat in front of you (4 going across).
2. Flip the pair (1,2) up and over on top of (3,4).
3. Flip the ONE square (2) up and over (1).
[Note: if step 3 won't go, start over, but flip the entire original shape
over (exposing the back).]
4. Flip the pair (2,4) up and over on top of (5,6).
5. Flip the pair (1,2) up and toward you on top of (blank,4).
6. Flip the ONE square (2) up and left on top of (1).
7. Flip the pair (2,4) up and toward you.
Your puzzle won't be completely solved, but this is how to get the shape.
Notice that 3,5,6,7,8 don't move.
==> games/scrabble.p <==
What are some exceptional scrabble games?
==> games/scrabble.s <==
The shortest scrabble game:
The Scrabble Players News, Vol. XI No. 49, June 1983, contributed by
Kyle Corbin of Raleigh, NC:
[J]
J U S
S O X
[X]U
which can be done in 4 moves, JUS, SOX, [J]US, and [X]U.
In SPN Vol. XI, No. 52, December 1983, Alan Frank presented what
he claimed is the shortest game where no blanks are used, also
four moves:
C
WUD
CUKES
DEY
S
This was followed in SPN, Vol. XII No. 54, April 1984, by Terry Davis
of Glasgow, KY:
V
V O[X]
[X]U,
which is three moves. He noted that the use of two blanks prevents
such plays as VOLVOX. Unfortunately, it doesn't prevent SONOVOX.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Record for the highest scrabble score in a single turn (in a legal position):
According to the Scrabble Players Newspaper (since renamed to
Scrabble Players News) issue 44, p13, the highest score for one
turn yet discovered, using the Official Scrabble Players
Dictionary, 1st ed. (the 2nd edition is now in use in club and
tournament play) and the Websters 9th New Collegiate Dictionary,
was the following:
d i s e q u i l i b r a t e D
. . . . . . . e . . . . . . e
. . . . . . . e . . . . . o m
r a d i o a u t o g r a p(h)Y
. . . . . . . . . . . w a s T
. . . . . . . . . . b e . . h
. . . . . . . . . . a . . g o
. . . c o n j u n c t i v a L
. . . . . . . . . . . . . n o
. . . . . . . f i n i k i n G
. . . . . . . a . . . (l) e i
. . . . . . . d . s p e l t Z
. . . . . . w e . . . . . . e
. . . . . . r . . . . . . o r
m e t h o x y f l u r a n e S
for 1682 points.
According to the May 1986 issue of GAMES, the highest known score achievable
in one turn is 1,962 points. The word is BENZOXYCAMPHORS formed across the
three triple-word scores on the bottom of the board. Apparently it was
discovered by Darryl Francis, Ron Jerome, and Jeff Grant.
As for other Scrabble trivia, the highest-scoring first move based on the
Official Scrabble Players Dictionary is 120 points, with the words JUKEBOX,
QUIZZED, SQUEEZE, or ZYMURGY. If Funk & Wagnall's New Standard Dictionary
is used then ZYXOMMA, worth 130 points, can be formed.
The highest-scoring game, based on Webster's Second and Third and on the
Oxford English Dictionary, was devised by Ron Jerome and Ralph Beaman and
totalled 4,142 points for the two players. The highest-scoring words in
the game were BENZOXYCAMPHORS, VELVETEEN, and JACKPUDDINGHOOD.
The following example of a SCRABBLE game produced a score of 2448 for one
player and 1175 for the final word. It is taken from _Beyond Language_ (1967)
by Dmitri Borgman (pp. 217-218). He credits this solution to Mrs. Josefa H.
Byrne of San Francisco and implies that all words can be found in _Webster's
Second Edition_. The two large words (multiplied by 27 as they span 3 triple
word scores) are ZOOPSYCHOLOGIST (a psychologist who treats animals rather
than humans) and PREJUDICATENESS (the condition or state of being decided
beforehand). The asterisks (*) represent the blank tiles. (Please excuse
any typo's).
Board Player1 Player2
Z O O P S Y C H O L O G I S T ABILITY 76 ERI, YE 9
O N H A U R O W MAN, MI 10 EN 2
* R I B R O V E I FEN, FUN 14 MANIA 7
L T I K E G TABU 12 RIB 6
O L NEXT 11 AM 4
G I AX 9 END 6
I T IT, TIKE 10 LURE 6
* Y E LEND, LOGIC*AL 79 OO*LOGICAL 8
A R FUND, JUD 27 ATE, MA 7
L E N D M I ROVE 14 LO 2
E A Q DARE, DE 13 ES, ES, RE 6
W A X F E N U RE, ROW 14 IRE, IS, SO 7
E T A B U I A DARED, QUAD 22 ON 4
E N A M D A R E D WAX, WEE 27 WIG 9
P R E J U D I C A T E N E S S CHIT, HA 14 ON 2
PREJUDICATENESS,
AN, MANIAC,
QUADS, WEEP 911 OOP 8
ZOOPSYCHOLOGIST,
HABILITY, TWIG,
ZOOLOGICAL 1175
--------------------------------------
Total: 2438 93
F, N, V, T in
loser's hand: +10 -10
--------------------------------------
Final Score: 2448 83
---------------------------------------------------------------------------
It is possible to form the following 14 7-letter OSPD words from the tiles:
HUMANLY
FATUOUS
AMAZING
EERIEST
ROOFING
TOILERS
QUIXOTE
JEWELRY
CAPABLE
PREVIEW
BIDDERS
HACKING
OVATION
DONATED
==> games/square-1.p <==
Does anyone have any hints on how to solve the Square-1 puzzle?
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