From: Truman Collins
Subject: Alphametic puzzles
An alphametic puzzle is an arithmetic problem involving words where there is a one-to-one mapping between letters and digits that makes the arithmetic equation true. For example:
I + BB = ILL (answer appears at the end of the next paragraph)
There is only one substitution of digits for letters where this is true in base 10. There are a couple of rules to these puzzles. A specific digit can only substitute for one letter and zero can't be used for a letter appearing on the far left. The only answer to this one is (I=1, B=9, L=0). Another more difficult one that is well known is SEND + MORE = MONEY.
Some time ago, I wrote a program to search for these puzzles from a group of words. I've found a lot of them so far and thought I'd post a few of them here. These have exactly one solution in base 10.
BILL + WILLIAM + MONICA = CLINTON GREEN + ORANGE = COLORS PACIFIC + PACIFIC + PACIFIC = ATLANTIC CASSATT + RENOIR = PICASSO MANET + MATISSE + MIRO + MONET + RENOIR = ARTISTS COMPLEX + LAPLACE = CALCULUS
I have a web page with more of these types of puzzle on it. It's at:
Truman Collins' Alphametic Puzzle Site
This site has a web-based solver for these puzzles, as well as a generator for these puzzles. Check it out!
There are two other great web pages for alphametic puzzles. They are:
The first has some very unusual types of these puzzles and the second has lots more puzzles as well as a wealth of links to related pages.
-Truman
From: Steve Clarke
Hi all -
I love cryptorithms, such as:
SEND
+ MORE
-----
MONEY
You know, the type where arithmetical sums, divisions, etc, are replaced by letters, and you have to solve for each of the letters ... Does any one know any good ones of these, to post here? or can anyone tell me of a place on the Net which might have them? I have a good book on them, but I need fresh puzzles :)
The following list should keep you busy for a while. To me, the most amazing creation of all is the second "chessametic" -- a cryptorithm that is also an interesting chess game.
ALAS + LASS + NO + MORE = CASH DONALD + GERALD = ROBERT CROSS + ROADS = DANGER RIDER + DROPS + REINS + HORSE = LOSES THIS + ISA + GREAT + TIME = WASTER FATHER + MOTHER = PARENT PIERRE + ELLIOTT = TRUDEAU APPLE + GRAPE + PLUM = BANANA WE + WANT + NO + NEW + ATOMIC = WEAPON PEANUT + TEETH = CARTER FIFTY + STATES = AMERICA TERRIBLE + NUMBER = THIRTEEN EARTH + AIR + FIRE + WATER = NATURE SATURN + URANUS + NEPTUNE + PLUTO = PLANETS GEORGIA + OREGON + VERMONT = VIRGINIA MONEY + POP + SOME + MONEY = PLEASE SAMS + IDEA + MADE = SENSE (The IDEA wasn't ODD!) SEE + YOU = SOON HEAR + THOSE + THREE = CHEERS HEAR + THAT + CHEER + AT + THE = FINISH NO + GUN + NO = HUNT MOON + MEN + CAN = REACH UK + USA + USSR = ABOMB OSAKA + HAIKU + SUSHI = JAPAN WINTER + BREEZE + BRED + BITTER = FREEZE. WINTER + IS + WINDIER, + SUMMER + IS = SUNNIER. NO + SNOW + IN + VIEW + ON + ROOFS + IN = VENICE. MARTIN + GARDNER = RETIRES. NATHAN + ATE + GREEN = PEPPERS. AMELIA + PEELED + A = BANANA. WHO + IS + THIS = IDIOT? ROMANS + ALSO + MORE + OR + LESS + ADDED = LETTERS. GEE, + I + SEE + A + RARE + MAGIC = SQUARE. ADAM + AND + EVE = MOVED OLD + SALT + TOLD + TALL = TALES LETTERS + ALPHABET = SCRABBLE WHEN + IN + ROME + BE + A = ROMAN ONCE + MORE + ONTO + THE = BEACH XMAS + MAIL + EARLY = PLEASE CALL + 1800 + 2385355 + FEDERAL = EXPRESS DIVER + DIVES + DEEP + IN = RIVER DID + HE + READ + HER = DIARY ADAM + SAYS + YES + IM + ADAM = MADAM BONGO + BONGO + BONGO + ON + THE = CONGO SUSIES + SISTER + SISSIE + SKIS + IN + SUSIES = BIKINIS PRETTY + POLLY + PARROT = REPEATS CRABBY + CRABBY + TABBY + MAY = SCRATCH REST + BREAK + AT + BAKER = STREET SMITHS + QUICK = TRICKS A + MERRY + XMAS = TURKEY FEMALES + AT + LAST + DEFEAT = EVEREST THIS + IS + VERY = EASY NEIL + A. + SEES = ALIEN (also a palindrome!)---------------------------------------------
The Doubly-True Genre
(true even when you add up the numbers corresponding to the words)
THREE + THREE + ONE = SEVEN NINE + LESS + TWO = SEVEN ONE + THREE + FOUR = EIGHT THREE + THREE + TWO + TWO + ONE = ELEVEN SIX + SIX + SIX = NINE + NINE TWO * TWO + EIGHT = TWELVE SEVEN + SEVEN + SIX = TWENTY ONE + ONE + ONE + THREE + THREE + ELEVEN = TWENTY EIGHT + EIGHT + TWO + ONE + ONE = TWENTY ELEVEN + NINE + FIVE + FIVE = THIRTY NINE + SEVEN + SEVEN + SEVEN = THIRTY TEN + SEVEN + SEVEN + SEVEN + FOUR + FOUR + ONE = FORTY TEN + TEN + NINE + EIGHT + THREE = FORTY FOURTEEN + TEN + TEN + SEVEN = FORTYONE NINETEEN + THIRTEEN + THREE + TWO + TWO + ONE + ONE + ONE = FORTYTWO FOURTEEN + THREE + TWO + ONE [22 times] = FORTYONE FORTY + TEN + TEN = SIXTY SIXTEEN + TWENTY + TWENTY + TEN + TWO + TWO = SEVENTY SIXTEEN + TWELVE + TWELVE + TWELVE + NINE + NINE = SEVENTY TWENTY + TWENTY + THIRTY = SEVENTY FIFTY + EIGHT + EIGHT + TEN + TWO + TWO = EIGHTY FIVE + FIVE + TEN + TEN + TEN + TEN + THIRTY = EIGHTY SIXTY + EIGHT + THREE + NINE + TEN = NINETY ONE + NINE + TWENTY + THIRTY + THIRTY = NINETY---------------------------------------------
"Found" Alphametics
I + THINK + IT + BE + THINE = INDEED (Hamlet, Act V, Scene 1) DOUBLE + DOUBLE + TOIL = TROUBLE (MacBeth) WHAT + WAS + THY = CAUSE? (King Lear, Act IV, Scene 4)----------------------------------------------
Chessametics
P-K4
P-K4
B-B4
P-R4
Q-B3
P-R4
QxP
----
IWIN
P-K4 + P-K4
+ N-KB3 + N-QB3
+ B-B4 + N-B3
+ P-Q4 + PxP
+ O-O + P-Q3
+ NxP + B-K2
+ N-QB3 + O-O
+ P-KR3 + R-K1
+ R-K1 + N-Q2
+ BxP + KxB
+ N-K6 + KxN
+ Q-Q5 + K-B3
+ Q-KB5 = BOOHOO
(this is actually an interesting game where a single tactical mistake gets punished by a 4-move mate sacrificial mate.)
-----------------------------------------
DAD + AND + SON + SAT + ON + SOD + DAD + STOOD + AT + NOON, + AND + SON + SOON + STOOD, + TOO + A + SAD + SON, + SANS + DAD, + STOOD + AND + STOOD. + NO + DAD. + A + SAD, + SAD = FINALE.
From a song
***********
MAKE + A + NEW + PLAN = STAN
HOP + ON + THE + BUS = GUS
DONT - NEED - TO - BE - COY = ROY
a haiku
*******
IN + ARCTIC + TERRAIN
+ AN + ANCIENT + EERIE + ICE + TRACT
+ I + ENTER + A + TRANCE = FLATIANA
A poem about the Sevvoth Island in the North Sea
************************************************
TEN + HERONS + REST + NEAR + NORTH + SEA + SHORE
+ AS + TAN + TERNS + SOAR + TO + ENTER + THERE
+ AS + HERONS + NEST + ON + STONES + AT + SHORE
+ THREE + STARS + ARE + SEEN
+ TERN + SNORES + ARE + NEAR = SEVVOTH
-------------------------------------
Problems involving multiplication or division
REASON = (IT)(IS) + THERE
MAD * MAN = ASYLUM
XXX * XX = XXXXX (each digit is a prime, no letters or digits are provided)
GO * ON = TROT
LYNDON * B = JOHNSON
HE * HE = SHE
MEN * AND = WOMEN
EVE/DID = .TALKTALK ...
COGITO = ERGO * SUM
FERMAT * S = LAST + THEOREM.
SEND / A = GIFT (A very ODD GIFT)
WINNIE / THE = POOH
X X X
-- + -- + -- = 1
XX XX XX
????
* ??7?
---------
?????
????
?????
---------------
????????
PUZZLE
* xxxxxxx
-------------
xxxxxxx
xWxxxxx
xxOxxxx
xWORLDx
xxxxLxx
xxxxxDx
xxxxxxx
-------------------------
xPxUxZxZxLxEx
(there is no restriction on the xs)
xxx
* xxx
-----
xxx
xxx
xxx
---------
xxxxx
(No digit occurs more than twice.)
x7xxx
________________
xxx ) xxxxxxxx
xxxx
-------
xxx
xxx
-----
xxxx
xxx
-----
xxxx
xxxx
----
xx8xx
__________
xxx ) xxxxxxxx
xxx
---
xxxx
xxx
---
xxxx
xxxx
----
(this last one can be figured out with almost no trial and error!)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
From: Jan Merolant
Newsgroups: rec.puzzles
Subject: Re: Cryptorithms
Date: Wed, 16 Dec 1998 20:04:39 +0100
Steve Clarke wrote:
I love cryptorithms, such as:
SEND
+ MORE
-----
MONEY
Here some more, which partly were made by Gijsbert van Uden
and partly by me. We made a lot of Dutch ones too.
Have fun..
Jan
I * DRANK + WHAT = AHRAHG (Socrates's dying words)
MASH + PEAR + GRAPE + APPLE = PUREE
DONT + STOP + THE = DANCE
FARTUS + ALOTUS + FARTS + AS = ROMANS
HEAR + THAT + CHEER + AT + THE = FINISH
HERE + THEY + GO = AGAIN
YKSI + AONO + EEN + ONE + EIN + UN = SEVEN
OSAKA + HAIKU + SUSHI = JAPAN
MACHU + PICCHU = INDIAN
MAKE + A + NEW + PLAN = STAN
HOP + ON + THE + BUS = GUS
DONT - NEED - TO - BE - COY = ROY
COGITO = ERGO * SUM ==> I think, therefore I am (Latin)
((JE + PENSE) - DONC) + JE = SUIS ==> I think, therefore I am ( French)
TWO * TWO + EIGHT = TWELVE
IT + IS + NOT + NO, + IS + IT + NOT, + OH + NO, + IT + IS + NOT = YES
SHE + KNOWS + HOW + IT = WORKS
SINOPE + ELARA + IO = EUROPA (four moons of Jupiter)
COPY + PASTE + SAVE = TOOLS