Alphametic

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"A mathematical puzzle consisting of a numerical computation with letters substituted for numbers which are to be restored through mathematical reasoning"[1] Furthermore, like all other forms of Verbal arithmetic, an alphametic must not contain any words beginning with zero, no single digit may be used for more than one letter and it must have only one solution.

Solving Alphametics[edit]

see Verbal arithmetic#Solving cryptarithms

Examples[edit]

Double True Alphametics[edit]

"ONE + NINE + TWENTY + FIFTY = EIGHTY (4)

TWO + FOURTEEN + FIFTEEN + TWENTY = FIFTYONE (4)

THREE + SEVEN + TEN + TWENTY + THIRTY = SEVENTY (4)

THREE + NINE + TEN + FOURTEEN + FIFTEEN = FIFTYONE (4)

FIVE + SIX + SIXTEEN + NINETEEN + TWENTY = SIXTYSIX (3)

SIX + NINE + ELEVEN + SIXTEEN + NINETEEN = SIXTYONE (3)

EIGHT + TEN + SIXTEEN + SEVENTEEN + EIGHTEEN = SIXTYNINE (5)

ONE + FIVE + TEN + ELEVEN + NINETEEN + FORTYFIVE = NINETYONE (3)

ONE + SEVEN + NINE + FIFTEEN + SIXTEEN + SEVENTEEN = SIXTYFIVE (5)

FIVE + SEVEN + ELEVEN + TWELVE + FIFTEEN + TWENTY = SEVENTY (5)

SIX + SEVEN + NINE + TWELVE + SIXTEEN + TWENTY = SEVENTY (5)

ONE + TWO + FIVE + NINE + ELEVEN + TWELVE + FIFTY = NINETY (5)"[2]

Alphametical Quotes[edit]

"AND + HAD + NO = SONS (3) (Numbers, 27:2)

AS + I + WAS + WITH = MOSES (2) (Joshua, 1:5)

AND + UNTO + MOUNT = HERMON (2) (Chronicles 1, 5:23)

THOUGH + HE + HATH = GAINED (2) (Job, 27:8)

WHEN + THERE + WERE + NO = DEPTHS (3) (Proverbs, 8:24)

WHOSE + TEETH + ARE + AS = SWORDS (4) (Proverbs, 30:14)

THAT + THY + SHAME + MAY = APPEAR (3) (Jeremiah, 13:26)

AND + ALL + HANDS + SHALL + BE = FEEBLE (3) (Ezekiel, 21:7)

THEN + JESUS + WENT = THENCE (2) (Matthew, 15:21)

AND + SAID + UNTO = SIMON (3) (Luke, 7:44)

WHICH + WAS + WITH + THE = FATHER (2) (John, 1:1)

STOOD + BEFORE + THE = THRONE (4) (Revelation of Saint John the Devine, 7:9)

SINCE + JULIUS = CAESAR (4) (Antony and Cleopatra)

HERE + SHE = COMES (2) (Much Ado about Nothing)

NOT + THIS = YOUTH (2) (CYMBELINE)

I + WILL + PAY + THE = THEFT (3) (Hamlet)

I + THINK + IT + BE + THINE = INDEED (3) (Hamlet)

THIS + IS + HIS = CLAIM (2) (Henry V)

AND + NEVER + HEARD = BEFORE (3) (Henry VI)

IF + THOU + DIDST + THIS + DEED + OF = DEATH (3) (King John)

NO + MAN + BEARS + SORROW = BETTER (3) (Julius Caesar)

WHAT + WAS + THY = CAUSE (2) (King Lear)

ILL + MAKE + ALL = SPEED (3) (Measure for Measure)

FOR + LACK + OF = TREAD (3) (A Midsummer Night's Dream)

AND + THE + DEATH + OF + A + DEAR = FRIEND (2) (A Midsummer Night's Dream)

HIS + HORSE + IS = SLAIN (2) (King Richard III)

I + THINK + HE + CANNOT = CHOOSE (4) (The Taming Of The Shrew)

HAD + I + A + GLASS + I = WOULD (3) (The Taming Of The Shrew)

O + THOU + TOUCH + OF = HEARTS (2) (The Life Of Timon Of Athens)

TIS + SAD + TITUS = CALLS (3) (The Tragedy Of Titus Andronicus)"[2]

Longest Known Alphametics (english)[edit]

Unknown - 29 addend: "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" (TVNREOHAS=987654321)[3]

Anton Pavlis - 1983 41 addends: "SO+MANY+MORE+MEN+SEEM+TO+SAY+THAT+THEY+MAY+SOON+TRY+TO+STAY+AT+HOME+ SO+AS+TO+SEE+OR+HEAR+THE+SAME+ONE+MAN+TRY+TO+MEET+THE+TEAM+ON+THE+MOON+AS+HE+HAS+AT+THE+OTHER+TEN=TESTS" (TRANHYSMOE=9876543210 ) [4]

Chris Pavlis - 2016 199 addends: THIS+A+FIRE+ THEREFORE+FOR+ALL+HISTORIES+I+TELL+A+TALE+THAT+FALSIFIES+ITS+TITLE+ TIS+A+LIE+ THE+TALE+OF+THE+LAST+FIRE+HORSES+ LATE+AFTER+THE+FIRST+FATHERS+FORESEE+THE+HORRORS+ THE+LAST+FREE+TROLL+TERRIFIES+THE+HORSES+OF+FIRE+ THE+TROLL+RESTS+AT+THE+HOLE+OF+LOSSES+ IT+IS+THERE+THAT+SHE+STORES+ROLES+OF+LEATHERS+ AFTER+SHE+SATISFIES+HER+HATE+OFF+THOSE+FEARS+ A+TASTE+RISES+AS+SHE+HEARS+THE+LEAST+FAR+HORSE+ THOSE+FAST+HORSES+THAT+FIRST+HEAR+THE+TROLL+FLEE+OFF+TO+THE+FOREST+ THE+HORSES+THAT+ALERTS+RAISE+THE+STARES+OF+THE+OTHERS+ AS+THE+TROLL+ASSAILS+AT+THE+TOTAL+SHIFT+ HER+TEETH+TEAR+HOOF+OFF+TORSO+AS+THE+LAST+HORSE+FORFEITS+ITS+LIFE+ THE+FIRST+FATHERS+HEAR+OF+THE+HORRORS+ THEIR+FEARS+THAT+THE+FIRES+FOR+THEIR+FEASTS+ARREST+ AS+THE+FIRST+FATHERS+RESETTLE+THE+LAST+OF+THE+FIRE+HORSES+ THE+LAST+TROLL+HARASSES+THE+FOREST+HEART+ FREE+AT+LAST+OF+THE+LAST+TROLL+ ALL+OFFER+THEIR+FIRE+HEAT+TO+THE+ASSISTERS+ FAR+OFF+THE+TROLL+FASTS+ITS+LIFE+SHORTER+AS+STARS+RISE+ THE+HORSES+REST+SAFE+AFTER+ALL+SHARE+HOT+FISH+ AS+THEIR+AFFILIATES+TAILOR+A+ROOFS+FOR+THEIR+SAFE=FORTRESSES (THIOFSRLAE=9876543210)

References[edit]

  1. ^ "Alphametic". Merriam-webster. Retrieved 14 December 2016. 
  2. ^ a b Collins, Truman. "tkcs-collins". Alphametic Puzzles. Retrieved 14 December 2016. 
  3. ^ Keith, Mike. "Sevveroth". Alphametics and Cryptarithms. Retrieved 14 December 2016. 
  4. ^ Pavlis, Anton. "Crux Mathematicorum" (PDF). Canadian Mathematical Society. Canadian Mathematical Society. Retrieved 14 December 2016. 

External links[edit]