From - Mon Nov 9 19:01:58 1998 Sender: Truman Collins From: Truman Collins Subject: Alphametic puzzles Newsgroups: rec.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 this type of puzzle on it. It's at: http://www.teleport.com/~tcollins/alphamet/alphamet.html I also wrote a web-based solver for these puzzles, which is at: http://www.teleport.com/~tcollins/alphamet/alpha_solve.html There are two other great web pages for alphametic puzzles. They are: http://members.aol.com/s6sj7gt/mikealp.htm http://www.geocities.com/Athens/Agora/2160/ 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 -- tcollins@teleport.COM Public Access User --- Not affiliated with TECHbooks Public Access UNIX and Internet at (503) 220-1016 (2400-14400, N81) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - From - Thu Dec 17 10:33:15 1998 From: rhoads@paul.rutgers.edu (Glenn) Newsgroups: rec.puzzles Subject: Re: Cryptorithms Date: 16 Dec 1998 20:09:36 -0500 Steve Clarke writes: >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 x 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 - Thu Dec 17 10:40:27 1998 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 E=MC2