Joseph S. Madachy explains cryptarithms and alphametic in "Madachy's Mathematical Recreations".

Cryptarithms are puzzles in which letters or symbols are substituted for the digits in an arithmetical calculation. Algebraic expressions might be regarded as cryptarithms of a sort, but algebra is not generally considered to be mathematically recreational. Cryptarithms have existed for centuries, and it is doubtful if it will ever be known when such puzzles were first devised. If a cryptarithm utilizes letters in place of the digits, and these letters form sensible words or phrases, the puzzle is termed an alphametic. J. A. H. Hunter coined the term in 1955.

Double True

General Bases

Arithmetical Restorations

All the digits

German Alphametics


Cross Number Puzzles (Arithmogriphs)


The numbers 1 - 26 have been randomly assigned to the letters of the alphabet. The numbers beside each word are the total of the values assigned to the letters in the word. e.g for LYRE L,Y,R,E might equal 5,9,20 and 13 respectively or any other combination that add up to 47.

The problem - What is the value of D ?

  BALLET   45      POLKA     59
  CELLO    43      QUARTET   50
  CONCERT  74      SAXOPHONE 134
  FLUTE    30      SCALE     51
  FUGUE    50      SOLO      37
  GLEE     66      SONG      61
  JAZZ     58      SOPRANO   82
  LYRE     47      THEME     72
  OBOE     53      VIOLIN    100
  OPERA    65      WALTZ     34
A problem form 'Tough Puzzles'. Solution

Mysterious Computation

Printers Errors

Equation Puzzles

Operator Puzzles


Alphametic and Cryptarithms Links

Cryptarithms Programs

Torsten Sillke

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Last Update: 2005-12-24