http://www.primepuzzle.com/leeslatest/alphameticpuzzles.html

# Lee's Latest

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:

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
```