Alphametics and Cryptarithms

Alphametics

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.

The classic one.
```
  S E N D
  M O R E
---------
M O N E Y
```
Does someone realy need a solution for this one?
Author: H.E. Dudeney in the July 1924 issue of Strand Magazine 68 (1924) 97, 214
Ref: Geoffrey Mott-Smith, Mathematical Puzzles, 1954, Problem 114
Ref: W. R. Ransom, One hundred Mathematical Curiosities, 1955, p120
Ref: Longley-Cook, New Math Puzzle Book, 1970, p53
Ref: E. P. McCravy, Mathematics Magazine 45 (1972) 48-49, number of solutions for base >= 10
Ref: Heinrich Hemme, Das Hexeneinmaleins, 2000, Problem 16, p16
I receive you loud and clear
```
    T H I S
      I S A
  G R E A T
    T I M E
-----------
W A S T E R
```
Ref: Unique solulion can be found in: AMM (1965) p316 E-1681

Planets

  S A T U R N
  U R A N U S
N E P T U N E
    P L U T O
-------------
P L A N E T S

Author: Willy Engren Ref: JoRM 12 (1979) 133-134

Planets

      M A R S
    V E N U S
  S A T U R N
  U R A N U S
-------------
N E P T U N E

Author: Willy Engren Ref: JoRM 13 (1980/81) 293

Health

H E A R T  +  E A R S  +  N O S E  +  T H R O A T  =  H E A L T H

Author: Richard I. Hess Ref: JoRM 21 (1989) 61 Alpha 1680

Hurray
```
H U R R A Y  +  H U Z Z A H  =  P U Z Z L E S
```
Author: Richard I. Hess Ref: JoRM 21 (1989) 137 Alpha 1698
Authority Figures
```
F A T H E R  +  M O T H E R  =  P A R E N T
```
Author: David J. Porter Ref: JoRM 21:4 Alpha 1743

Greenhouse Effect

W I N T E R + I S + W I N D I E R + S U M M E R + I S = S U N N I E R

Author: Brian Barwell Ref: JoRM 21:3 Alpha 1809

Rhyme's Pertner
```
R E A S O N  =  (I T)(I S)  +  T H E R E
```
Author: Robert B. Israel Ref: JoRM 21:3 Alpha 1731, (explained solution)
Funny Farm
```
M A D  *  M A N  =  A S Y L U M
```
Author: Robert B. Israel Ref: JoRM 21:4 Alpha 1751, (explained solution)
Mad
```
A L F R E D  /  E  =  N E U M A N
A L F R E D  *  E  =  N E U M A N
```
These are two base-9 problems.
Ref: Joseph S. Madachy, Madachy's Mathematical Recreations, 1979, p193
Eve double talked
```
eve/did = .talktalktalk...
```
There are 2 solutions here. One of them with a reduced fraction.
Ref: Martin Gardner, Mathematical Circus, 1979, Chap. 11
Ref: Joseph S. Madachy, Madachy's Mathematical Recreations, 1979, p191
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 31
For tired readers?
```
  T H E S E
  T E A S E
  T I R E D
-----------
R E A D E R
```
Author: Hunter Ref: Joseph S. Madachy, Madachy's Mathematical Recreations, 1979, p185
Adam and Eve
```
  A D A M
    A N D
    E V E
---------
M O V E D
```
Ref: J. A. H. Hunter, Entertaining Mathematical Teasers, 1983, p93
addition and subtraction
```
S Q U A R E
  D A N C E
-----------
D A N C E R
```
This problem has two solutions: one as an addition problem, the other as subtraction.
Ref: Joseph S. Madachy, Madachy's Mathematical Recreations, 1979, p191
related to Canada
```
P I E R R E  +  E L L I O T T  =  T R U D E A U
```
Ref: Dick Hess, Puzzles from around the world, 1997, Problem 6
fruits
```
A P P L E  +  G R A P E  +  P L U M  =  B A N A N A
```
Ref: Dick Hess, Puzzles from around the world, 1997, Problem 13
```
A P P L E  +  L E M O N  =  B A N A N A
```
Author: Col. G. L. Sicherman
peace
```
W E  +  W A N T  +  N O  +  N E W  +  A T O M I C  =  W E A P O N
```
Ref: Dick Hess, Puzzles from around the world, 1997, Problem 16
a president from USA
```
P E A N U T  +  T E E T H  =  C A R T E R
```
Solve this alphametic in base 10 and base 9.
Ref: Dick Hess, Puzzles from around the world, 1997, Problem 43
The Digital Atom Smasher
```
sqrt(ATOM)  =  A + TO + M
```
this has two solutions
Ref: Angela Fox Dunn, Mathematical Bafflers, 1980, p39

T E R R I B L E  +  N U M B E R  =  T H I R T E E N

Author: Steven Kahan

Right and Wrong
```
Z E R O E S
    O N E S
-----------
B I N A R Y
```
Author: Peter Macdonald, 1977
Ref: JoRM 10 (1977) 155
Right and Wrong
```
W R O N G
W R O N G
---------
R I G H T
```
this has two solutions under the restriction of O = zero.
Ref: Angela Fox Dunn, Mathematical Bafflers, 1980, p103
palindromic
```
N O R A  *  L  =  A R O N
```
Ref: Martin Gardner, Mathematical Magic Show, 1977, Chap 15, Problem 2

Scrabble

A L P H A B E T
  L E T T E R S
---------------
S C R A B B L E

Ref: G. Brandreth, The Puzzle Mountain, 1981, p61

Scrabble

  N A I L O R
  L I N G E L
-------------
F A C E O F F

Ref: rec.puzzles

an easy one
```
A  *  (W E B T V)  =  D D D D D D
```
Ref: rec.puzzles
Mathematicians
```
  G A U S S
  R I E S E
-----------
E U K L I D
```
Ref: Zweistein; 99 Logeleien von Zweistein, 1969, Problem 55
The values of G and R are exchangeable.
trigonometry (French)
```
S I N ²  +  C O S ²  =  U N I T E
```
Ref: rec.puzzles
how many drinks do you need?
```
ALCOHOL + ALCOHOL + ... + ALCOHOL = HANGOVER
```
how many drinks do you need?
Ref: rec.puzzles
Chinese calendar
```
H A P P Y  -  T I G E R  =  Y E A R
```
Solve this under the conditions that
1. TIGER being the third in the order of 12 animals (rat, ox, tiger, rabbit, dragon, snake, horse, ram, monkey, cook, dog, boar), the number represented by TIGER divided by 12 gives a remainder 3 and
2. as there are 10 possible digits to fill in the 9 letters that appear in this alphametic problem, there is bound to be one digit missing. However, the missing digit turns out to be the remainder if the number represented by YEAR is divided by 12.
Author: Liang-shin Hahn (1986)
Ref: Liang-shin Hahn; Complex Numbers and Geometry, MAA, 1994, p186
Diamond
```
B O B B Y  +  L O V E D  =  J E W E L S
```
Ref: Ravi Narula, Brain Teasers, 1976, Jaiko Publ. House, p97
He or She
```
H E  *  H E  =  S H E
```
Author: M. E. Larsen
Ref: J. Lehmann, Mathe mit Pfiff, Manz Verlag 1977, p71 (P11: AB*AB=CAB)
The ABC
```
B A  *  C B A  =  D C B A
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
Aphis
```
T H I S  *  I S  =  A P H I S
```
This one has three solutions.
Author: A. G. Bradbury
Ref: JoRM 3:1 (Jan 1970) 49, Problem 68 (Solution of Underwood Dudley)
Puzzleland (Kindergarten) Algebra
```
  J G D C H
  I F A B E
-----------
B I B D E B
```
Ref: Sam Loyd, Cyclopedia of Puzzles, 1914, p238

Elements of Nature

E A R T H  +  A I R  +  F I R E  +  W A T E R  =  N A T U R E

Author: Herman Nijon
Ref: JoRM 9 (1977) 207

square
```
T W O  *  T W O  =  S Q U A R E
```
Ref: H. E. Dudeney, Strand 78 (1929) 91, 208
Hawaii
```
NIIHAU ± KAUAI ± OAHU ± MOLOKAI ± LANAI ± MAUI ± HAWAI = 0
```
Ref: Donald E. Knuth; The Art of Computer Programming, Section 7.2.1.2 Exc. 26.
directions
```
N O R T H / S O U T H  =  E A S T / W E S T
```
Ref: Nob Yoshigahara; JoRM 27 (1995) 137
Prime factors
```
A B C B A  =  D  *  B E  *  B F F A
```
The factors shall be prime numbers.
Ref: Ken Russell, MENSA Magazine Oct. 1996, p28
The Solution
A Facetious Division
```
A H H A A H / J O K E  =  H A
```
Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 19.

Double True

what is the sum

    F I V E
    F I V E
    N I N E
E L E V E N
-----------
T H I R T Y

Ref: Ken Russell, MENSA Magazine Oct. 1996, p28

what is the sum (french)
```
  V I N G T
    C I N Q
    C I N Q
-----------
T R E N T E
```
Author: Alan Wayne
Ref: M. Gardner, Sci. Am. (Dec. 1975), p116
what is the sum (german)
```
  E I N
  E I N
  E I N
  E I N
-------
V I E R
```
Author: Alan Wayne
Ref: M. Gardner, Sci. Am. (Dec. 1975), p116
The Solution
Das stimmt sogar (german)
```
  S E C H S
  S E C H S
-----------
Z W O E L F
```
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 48
(spanish)
```
U N O  +  U N O  +  T R E E  =  C I N C O
```
This one has several solutions. The Solution
Dr. Matrix
```
S I X  +  S I X  +  S I X  =  N I N E  +  N I N E
```
Author: Alan Wayne
Ref: M. Gardner, Sci. Am. (Sep. 1975),
M. Gardner, The Magic Numbers of Dr. Matrix, 1985
Chap. 18: The King James Bible
The Solution
Dr. Matrix in New York
```
F O R T Y  +  T E N  +  T E N  =  S I X T Y
```
Ref: Longley-Cook, New Math Puzzle Book, 1970, p54
Ref: M. Gardner, The Magic Numbers of Dr. Matrix, 1985
Chap. 1: New York
Note: ELEVEN + TWO is an anagram of TWELVE + ONE.
The Solution
true and false
```
T W O  *  T W O  =  T H R E E
```
Author: H.E. Dudeney in the July 1924 issue of Strand Magazine
0123
```
T H R E E  =  T W O  +  O N E  +  Z E R O
```
Ref: Richard L. Breisch; Recreational Math. Magazine 12 (Dec. 1962) 24

General Bases

base eleven
```
  U N I T E D
  S T A T E S
-------------
A M E R I C A
```
Ref: L. A. Graham; The surprise Attack in Mathematical Problems, 1968, Problem 9
Ref: L. A. Graham; Mathematik aus dem Hinterhalt, 1981, Problem 9
Fair Fares
```
F A R E S  =  F E E ²
```
Solve this alphametic in base 6.
Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 235.
Number system unknown
```
K Y O T O
K Y O T O
K Y O T O
---------
T O K Y O
```
Which number system has a solution? Author: V. Dubrovsky, A. Shvetsov
Ref: Quantum, Brainteaser B144 Quantum CyberTeaser May/June 1995 or Quantum CyberTeaser May/June 1995 (local)
venusean arithmetic
```
U V  +  U V  =  U W U
```
Author: Harry L. Nelson
Ref: Martin Gardner, Mathematical Magic Show, Alfred A. Knopf (1977) New York, Chap. 8 Finger Arithmetic, Fig. 32
unique base
Examples of problems which are solvable only in one base b.
```
X  +  X  +  X  =  X X
```
Solution: 3 X = b X + X. Thus 2 X = b X and as X not equal 0 we have b = 2. Now X = 1.
```
X Y  +  X X  =  X Y X
```
Solution: The last digit shows Y = 0. Dropping the last digit we again get 2 X = b X.
commutator
```
A B  -  B A  =  A
```
Ref: J. Lehmann, Mathe mit Pfiff, Manz Verlag 1977, p71 (P15: AB-BA=A)

Arithmetical Restorations

A prime cryptarithm
```
    X X X
      X X
    ----- *
  X X X X
X X X X
---------
X X X X X
```
In this remarkable cryptarithm, each digit is a prime (2, 3, 5 or 7). No letters or digits are provided as clues; but there is only one solution.
Ref: B. A. Kordemsky, The Moscow Puzzles, 1972, Problem 273
Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 123
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 20
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p130
The following variation has other solutions.
```
X X X  *  X X  =  X X X X X
```

4 digits

      x x x
      x 2 x
      ----- *
      x x x
  x x x x
  x 8 x
-----------
x x 9 x 2 x

Ref: B. A. Kordemsky, The Moscow Puzzles, 1972, Problem 272 b

3 digits
```
    x x x
      x x
    ----- *
    x x x
  x x 4
---------
x x x 0 1
```
Author: Arthur Haas
Ref: AMM 40 (Dec. 1933) 607-608 E-37, explained solution
An atomar square
```
A T O M  *  A T O M  =  x x x x A T O M
```
Ref: Sphinx - Nov 1933 #167 - Page 167 (by M. Pigeolet) saying TOCK TOCK = xxxxTOCK.
Ref: B. A. Kordemsky, The Moscow Puzzles, 1972, Problem 272 g
Ref: W. Engel (Ed.), Mathematische Olympiade-Aufgaben, 1979, A.2.42
Ref: M. Gardner, The Magic Numbers of Dr. Matrix, (1985) Chapter 4: Squaresville
Automorphic numbers: n^2 ends with n in base d. base 10: ...8212890625, ...1787109376.
A related problem is
```
H E  *  H E  =  S H E
```
Cryptic Multiplication
```
  O E E
    E E
------- *
E O E E
E O E
-------
O O E E
```
All even digits are replaced with E and all odd with O. What was the multiplication?
Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 233.
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 21
The Solution
Even Odd Multiplication
```
    E E O
      O O
--------- *
  E O E O
  E O O
---------
O O O O O
```
All even digits are replaced with E and all odd with O. What was the multiplication?
Author: Fitch Cheney
Ref: M. Gardner; Scientific American 207 (Oct 1962) 132, (Nov 1962) 162
Ref: H. Hemme; Die Quadrate des Teufels, (2003) Problem 98.
Even Odd Multiplication
```
    E O E E
      E O E
----------- *
    O O E E
O E O E E
E O O E
-----------
E O O O E E
```
All even digits are replaced with E and all odd with O. What was the multiplication?
Ref: Zweistein, Logeleien fuer Kenner, 1974, Problem 21
Ref: D. St. P. Barnard, O. Botsch; Hirnverzwirner, 1975, Problem 92

the wrong printer

        ? ? ? ?
        ? ? 7 ?
      ---------  *
      ? ? ? ? ?
      ? ? ? ?
  ? ? ? ?
---------------
? ? ? ? ? ? ? ?

Only digit 7 is printed.
Ref: Zeit Magazin, Nr 35, 22. Aug. 97, p42, Logelei

the wrong typewriter
```
    ? ? 3
    ? ? 3
    -----  *
    3 ? ?
  ? 3 ?
? ? 3
---------
? ? ? ? ?
```
Only digit 3 is printed.
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 26

this is too hard

    T H I S
        I S
  ---------  *
  x x T O O
H A R D x
-----------
x x x x x x

Ref: Joseph S. Madachy, Mathematics on Vacation, 1966, p192

puzzle world

              P U Z Z L E
            x x x x x x x
            -------------  *
            x x x x x x x
          x W x x x x x
        x x O x x x x
      x W O R L D x
    x x x x L x x
  x x x x x D x
x x x x x x x
-------------------------
x P x U x Z x Z x L x E x

Ref: Puzzle World, Ed. Nob Yoshigahara and Richard Bozulich, Ishi Press, Summer 1992, Pilot Edition.

Est modus in rebus

              E S T M O D U S
                I N R E B U S
            -----------------  *
            x x x x x x x x x
          x x x x x x x x x
          x x x x x x x x
      x x x x x x x x x
    x x x x x x x x x
  x x x x x x x x x
x x x x x x x x x
-----------------------------
x x x x x x x x I N R E B U S

Each of the ten digits corresponds to at least one letter, so there is precisely one case where two different letters are replaced by the same digit. Fred. Schuh admits that the puzzle is far from easy.
Ref: Fred. Schuh, The Master Book of Mathematical Recreations, Dover Publ. 1968, p315-317

Ancient

x x x ) x x x x x x ( x x x
        x 0 x x
        -------
          x x x x
          x 5 0 x
          -------
              x x x
              x 4 x
              =====

Ref: American Mathematical Monthly (1921) p37
Ref: Rouse Ball, Mathematical Recreations and Essays, Chapter I
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Vorwort

x x ) x x x x 3 x ( x x x x.x x
        x x
        ---
        4 x x
        x x x
        -----
            x x
            x x
            ---
              x x
              x x
              ---
                x x x
                x x x
                =====

Ref: Zweistein; 88 neue Logeleien von Zweistein, 1983, Problem 64

The three 5

x x x ) 5 x x x x x x x x ( x x x x x x x
        x x x
        -----
            x x x x
              x x x
              -----
                  5 x x
                  x x x
                  -----
                  x 5 x x
                  x x x x
                  =======

Ref: Zweistein; 88 neue Logeleien von Zweistein, 1983, Problem 19

The seven 7

x x x x 7 x ) x x 7 x x x x x x x ( x x 7 x x
              x x x x x x
              -----------
              x x x x x 7 x
              x x x x x x x
              -------------
                  x 7 x x x x
                  x 7 x x x x
                  -----------
                  x x x x x x x
                  x x x x 7 x x
                  -------------
                      x x x x x x
                      x x x x x x
                      ===========

Author: W. E. H. Berwick
Ref: W. E. H. Berwick; School World, 8 (July and October 1906) 280+320
Ref: Heinrich Dörrie; Triumpf der Mathematik, Sect 4 (p9-13)
Ref: Rouse Ball, Mathematical Recreations and Essays, Chapter I

The seven 7

x x x x 7 x x ) x x x x x x 7 x x x x x x x x x ( x x x 7 x x x x x x
                x x x x x x x
                -------------
                x x x x x x x x
                x x x x x x x x
                ---------------
                  x x x x x x x x
                    x x x x x x x
                  ---------------
                      x x x x x x x
                      x x x x x x x
                      -------------
                      x x x x x x 7 x
                        x x x 7 x x x
                      ---------------
                        x x x x x x x x
                        x x x x x x x x
                        ---------------
                          x x x x x x x x
                            x x x x x x x
                          ---------------
                                x 7 x x x x x
                                x x 7 x x x x
                                -------------
                                  x x x x x x x
                                  x x x x x x x
                                  -------------
                                              x

Ref: Fred. Schuh, The Master Book of Mathematical Recreations, Dover Publ. 1968, p318-320

The lonesome 7

x x x ) x x x x x x x x ( x 7 x x x
        x x x x
        -------
            x x x
            x x x
            -----
            x x x x
              x x x
            -------
                x x x x
                x x x x
                =======

Ref: American Mathematical Monthly 49 (1932) 489

The lonesome 8
```
x x x ) x x x x x x x x ( x x 8 x x
          x x x
        -------
            x x x x
              x x x
            -------
                x x x x
                x x x x
                =======
```
Author: P. L. Chessin
Ref: American Mathematical Monthly (Apr. 1932)
Ref: W. B. Carver, American Mathematical Monthly (Dec. 1954) 712
Ref: W. R. Ransom, One hundred Mathematical Curiosities, 1955, p134
Ref: Martin Gardner; The Second Scientific American Book of Mathematical Puzzles and Diversions, 1961, Chap. 14
Ref: L. A. Graham; The surprise Attack in Mathematical Problems, 1968, Prob. 31
Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 31
Ref: P. v Delft & J. Botermans, Creative Puzzles of the World, p161
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 36

The lonesome 8 again

x x x ) x x x x x x x x ( x x x x x
          x x x
        -------
              x x x x
                x x x
              -------
                x x x x
                8 x x x
                =======

Ref: W. Engel (Ed.), Mathematische Olympiade-Aufgaben, 1979, A.2.42
- 2. Math. Olympiade DDR, 1962/1963, Klasse 9, Stufe 1

A fairly easy lonesome 8

x x ) x x x x x x x x x x ( x x x x x 8 x x
      x x x
      -----
          x x x
          x x x
          -----
            x x x
            x x x
            -----
                  x x
                  x x
                  ---
                    x x x
                    x x x
                    =====

Ref: B. A. Kordemsky, The Moscow Puzzles, 1972, Problem 272 f

The eight 8

8 x x x ) 8 8 x x x x x x ( x x x x
          x x x x x
          ---------
            x x x x x
            x x x x x
            ---------
              x 8 x x x
              8 x x x 8
              ---------
                x x x x x
                x x x 8 8
                =========

Ref: Zeitschrift Archimedes, vor 1950
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p129

completely hidden

x x ) x x x x ( x x.x x x
        x x
        ---
        x x x
          x x
        -----
            x x
            x x
            ---
            x x x
            x x x
            -----
                x x
                x x
                ===

Ref: Joseph S. Madachy, Mathematics on Vacation, 1966, p192

completely hidden II

x x ) x x   ( x.x x x x
        x x
        ---
        x x x
        x x x
        -----
          x x x
          x x x
          -----
              x x
              x x
              ===

Ref: Zweistein, Logeleien für Kenner, 1974, Problem 7

nothing

x x x ) x x x x x x ( x x x x.x x x x
        x x x
        -----
            x x x
            x x x
            -----
              x x x
              x x x
              -----
                x x x
                x x x
                -----
                    x x x x
                    x x x x
                    =======

Author: A. Corrigan in Strand Magazine
Ref: H. E. Dudeney, The Strand Magazine 65 (1923) 311-312, 405, 538
Ref: P. v Delft & J. Botermans, Creative Puzzles of the World, p161
Ref: Heinrich Hemme, Der Wettlauf mit der Schildkröte, Problem 44

nothing else

x x x ) x x x x x x x x ( x x x x x x
        x x x
        -----
        x x x x
          x x x
        -------
              x x x x
                x x x
              -------
                x x x x
                x x x x
                =======

Determine the unique divisor.
Ref: H. Hemme & M. Schwoerer, Mathematischer Denkspass, 1998, p139

the complete ghost

x x x ) x x x x x x x x x ( x x x x x x
          x x x
        -------
              x x x x
                x x x
              -------
                  x x x
                  x x x
                  -----
                  x x x x
                  x x x x
                  =======

x x ) x x x x x x ( x x x x x
      x x
      ---
        x x x
          x x
        -----
          x x x
          x x x
          -----
            x x x
            x x x
            =====

The six-digit quotient of the first must be equal the dividend of the second.
Ref: H. E. Dudeney, Puzzles and Curious Problems, 1931, 36-37, 141.
Ref: Geoffrey Mott-Smith, Mathematical Puzzles, 1954, Problem 122

Sense of humore
```
x x ) x x x x 0 x ( x x x x
        x x
      -----
          x x x
          x x 1
          -----
              x x
              2 x
              ===
```
Ref: L. A. Graham; The surprise Attack in Mathematical Problems, 1968, Problem 9
Ref: L. A. Graham; Mathematik aus dem Hinterhalt, 1981, Problem 9

A Faded Document

x x ) x x x x 0 x ( x x x x
        x x
      -----
          x x x
          x x 1
          -----
              x x
              3 x
              ===

Ref: Ch. W. Trigg, Mathematical Quickies, 1985, Problem 173

It sounds greek to me
```
x x  +  x  =  x
```
Author: Jaime Poniachik
Ref: www.g4g4.com

All the digits

all digit sums
```
X X X  +  X X X  =  X X X
```
Put 1-9 once each to make the equation honest. Ref: Recreational Mathematics Magazine, No. 7 (Feb. 1962) 35-36
fractions with digits 1-9
```
 X     X     X
--- + --- + ---  =  1
X X   X X   X X
```
Put 1-9 once each to make the equation honest. Ref: REC 8:5 (1993) 5-6 (Nob)
Ref: L. Mittenzwey, Mathematische Kurzweil, Leipzig und Wien, 1880, Problem 141
multiply and add
```
X X
  X
---  *
X X
X X
---  +
X X
```
Put 1-9 once each to make the equation honest.
Author: H. E. Dudeney
Ref: M. Gardner's Sixth Book of Mathematical Games from Scientific American, 1971, Chap. 6.7 Three Cryptarithms
Ref: P. v Delft & J. Botermans, Creative Puzzles of the World, p161
All the digits
```
X X X X X  =  k  *  X X X X X
```
Put 0-9 once each to make the equation honest for k=7 and for k=9.
Let s(k) be the number of solutions without leading zero. David Daykin computed the table
```
   k  :  2  3  4  5  6  7  8  9
 s(k) : 48  6  8 12  0  1 16  3
```
Ref: Angela Fox Dunn, Mathematical Bafflers, 1980, p99 (k=9)
Ref: Angela Fox Dunn, Second Book of Mathematical Bafflers, 1980, p21 (k=7)
Ref: David Daykin, Mathematics Magazine, 42 (1969) 102-103 (k=2..14, base=3..15)
Ref: M. Gardner, The Magic Numbers of Dr. Matrix, 1985
Chap. 13: The Moon (k=7 and the table of s(k))
```
X X X X X  =  k  *  X X X X
```
Put 1-9 once each to make the equation honest for k=2..9.
Ref: H. E. Dudeney, Amusements in Mathematics, 1958, problem 88
Ref: P. v Delft & J. Botermans, Creative Puzzles of the World, p160
Years
```
X X X X X X X  /  X X X  =  1984
```
Put 0-9 once each to make the equation honest.
Ref: Stewart Metchette, Years Expressed as Distinct-digit Fractions, JoRM 13:1 (1980-81) 26-28
A Curious Multiplication
```
    x x x
    x x x
    -----  *
    x x x
  x x x
x x x
---------
x x x x x
```
No digit occurs more than twice.
Ref: Fred. Schuh, The Master Book of Mathematical Recreations, Dover Publ. 1968, p287-291
Ref: M. Gardner's Sixth Book of Mathematical Games from Scientific American, 1971, Chap. 6.7 Three Cryptarithms
Multiplication: fill in the digits
```
X O X O X  *  O X O X O  =  X O X O X O X O X O
```
All of the X's are different, as are all of the O's, as are all digits in the product (whose final O is 0).
Author: Jim Ferry
Ref: rec.puzzles 1999-06

German Alphametics

Kinderleicht?
```
  B A C K E
  B A C K E
-----------
K U C H E N
```
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 47
A family problem
```
  V A T E R
M U T T E R
-----------
E L T E R N
```
Ref: J. Lehmann, Mathe mit Herz, Urania (1991), p82, problem 22
Ref: J. Lehmann, Mathe mit Pfiff, Manz Verlag 1977, p72, problem 22
Ref: W. Engel (Ed.), Mathematische Olympiade-Aufgaben, 1979, A.2.43
There are 6 solutions
Patriot of Lippe, (don't be angry about this one.)
```
    L A G E
  L E M G O
-----------
S C H O E N
```
Author: Ingo Althöfer
soluble in base 12.
Patriot of Lage-Lippe
```
    L A G E
  L I P P E
-----------
S C H O E N
```
Author: Torsten Sillke (but the Patriot is Udo Sprute)
unique soluble in base 11.

Suche nach Atlantis

A T L A N T I S  =  S C H L A M M  +  S C H L I C K

Stern Nr. 13 (1996)

Auf den ersten Blick
```
Z W E I  +  B L I T Z  =  L I E B E
```
Stern Nr. 17 (1996)
Auf den ersten Blick II
```
Z W E I  +  B L I T Z  =  E R O T I K
```
Stern Nr. 18 (1996)

Steithammel, Streithähne

H A M M E L  +  H A E H N E  =  S T R E I T

Stern Nr. 18 (1996)

Kulturerlebnisse
```
M U S I K  +  K U N S T  =  G E N U S S
```
Stern Nr. 35 (1996) (several solutions)

Olympia'96

A T L A N T A  =  R U M M E L  +  P L E I T E N

Stern Nr. 37 (1996)

suchen und finden

S U C H E N  -  M A C H T  =  S P A S S

N A M E N  =  S C H A L L  -  R A U C H

Two solutions but "schall" is unique.

F I N D E  +  D I E S E  =  K I N D E R

M A C H  *  M A L  =  L A U T E R

K E I N E  +  A N G S T  =  S I G R I D

Ref: Zeit Magazin, Nr 47, 15. Nov. 1996, p51, Logelei

Kai und Ina

I N A  *  I S T  =  S U E S S

V I E L E N  :  D A N K  =  K A I
V E E V
---------
  A V U E
  A L K O
  ---------
    I N U N
    I N U D
    -------
          K

D E I N E  +  B E I N E  =  S U P E R

This alphametic has two solutions but the sum remains equal. What number is SUPER?

N I E M A N D  :  Z U  =  H A U S E
N I H
-------
    I M A
    I N S
    -------
      Z I N
      U D M
      -------
        N H D
        N H D
        =====

K U S S  +  L U S T  =  O L A L A

Ref: Zeit Magazin, Nr 23, 30. Mai 1997, p42, Logelei

no magazin any more

D I E  *  Z E I T  =  R A E T S E L

D E N K E R  +  G E R N E  =  L O G E L N

Ref: Zeit Nr 20, 12. Mai 1999, Logelei

Trinken

      S E K T * B I E R
      -----------------
    T B T S R
  B E R A S
S E K T I
-------------
S A E U F E R

Ref: Zeit Magazin, Nr 23, 30. Mai 1997, p42, Logelei

tierisch

S C H W I M M T  :  E I N  =  F I S C H
S N E I
---------
  I C I I
    E I N
  ---------
    C E T M
    C H F T
    ---------
      C M W M
      H C S C
      ---------
        H C C T
        N S C W
        -------
          E M S

Ref: Zeit Magazin, Nr 35, 22. Aug. 1997, p42, Logelei

schlau und klug?
```
U N S E R  +  O S C A R  =  S C H L A U
```
```
K L U G E  +  L E U T E  =  L O G E L N
```
Ref: Zeit Magazin, Nr 35, 22. Aug. 1997, p42, Logelei
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 77
jeder liebt es
```
J E D E R  +  L I E B T  =  B E R L I N
```
This alphametic has two solutions, but EIN BIER is unique.
Ref: Zeit Magazin, Nr 35, 22. Aug. 1997, p42, Logelei
sparen
```
W A I G E L  +  S P A R E  =  E I F R I G
```
Ref: Zeit Magazin, Nr 3, 10. Jan. 1997, Logelei
Wer ist Zweistein?
```
W E R  +  I S T  +  Z W E I  =  S T E I N
```
This alphametic has two solutions,
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 75

Musicmetic

bad music
```
+ C E G E F e c
+ C c B A D B c
+ C E G A F D c
---------------
c c d d B f f C
```
One frequency is false and must be corrected!
Ref: Zeit Magazin, Nr 38, 30. Sep. 1994, p44, Logelei

Cross Number Puzzles (Arithmogriphs)

 ABC *   DA = BEFA
  +      *      -
GHHA +  GJE = GFDC
------------------
GJEJ + HJJJ = FFDC

Ref: M Sändig, Hobbymatik, 1984, Titelpage
The Solution of Matthew Daly.

ABCD :  EFG =   HC
  -      *      +
 FHA -   IG =  FJD
------------------
AHBE - ACFE =  FAJ

Ref: Hör Zu, 17/1972
The Solution of H. Müller-Merbach.

 ABC *   DE = CFGH
  +      *      -
JDHJ +  DGC = JGKK
------------------
JEDK + EBAH = FAGH

Ref: Hör Zu, 38/2001
The Solution

  AB *  CDC = BABE
  *      +      -
 AFD + GHJE = GGDC
------------------
HFKH + GJEF = KDAH

Ref: Hör Zu, 10/1995
The Solution

 EGA *   AH = DGFG
  *      +      -
  LL + EFFC = EFDL
------------------
ABCD + EFGH = KLBK

Ref: Hör Zu, 00/1995
The Solution

ABAC :  DEF =   GB
  -      +      *
HEGF - HBID =  HED
------------------
EKBI - HKGI = ICDC

Ref: Hör Zu, 45/2002
The Solution

ABBC :  DDE =   DF
  +      +      *
AGFG - AHIB =  KKG
------------------
KGEH + ACKE = FCII

Ref: Hör Zu, 29/2003
The Solution

ABCD + DCEF = GHFI
  -      :      +
AHGE +  AIC = AKGF
------------------
 KEG *   KI = EBKB

Ref: Hör Zu, 31/2003
The Solution

ABCD + EBFG = FDBH
  :      -      +
  AE + EBII = EBAE
------------------
 AHC *   FG = KFGK

Ref: Hör Zu, 37/2003
The Solution

ABCD - EABF = GDGA
  :      -      -
 HII + EGKD = EFCK
------------------
  IH *  EDH = HABF

Ref: Hör Zu, 51/2003
The Solution

ABCD + EFCF = BGHE
  -      :      +
AAIF +  GDE = AEDC
------------------
 FCH *   GK = KHHI

Ref: Hör Zu, 01/2004
The Solution

ABBC :   DE =  FGD
  -      +      *
FBHI - FGKD =   FD
------------------
EHGI - FBCG = CCEK

Ref: Hör Zu, 05/2004
The Solution

ABCD + EFGG = HEBG
  :      -      +
  CI + EHKI = EFCH
------------------
 CKB *   GH = IKFD

Ref: Hör Zu, 07/2004
The Solution

ABCD :   EE =  EFD
  +      +      *
GHEH - GIKC =   IF
------------------
HHDI + GICF = DBCA

Ref: Hör Zu, 53/2004
The Solution

ABCD + EFGH = KLBK
  :      -      +
  LL + EFFC = EFDL
------------------
 EGA *   AH = DGFG

Robert Israel solved it with a Maple Program.
The Solution

ABCDE - FGEE = AHBDE
   :      -       -
   DI *  HDB =  BKDB
--------------------
  CDE + FKCD =  KDGD

Ref: Lehmann
The Solution

```
ATU + IAS  = IITE
 -     -       :
NEG : IOG  =    E
-----------------
PAU -  NS  =  PPA
```
Ref: Boris A. Kordemsky, Köpfchen muss man haben, 1975, P241
The Solution If you order the letters according there values you get a mathematical term in russian.
```
HEB + EUS  =  LFS
 -     -       :
WUB :  EH  =   US
-----------------
EHB - ESU  =   RA
```
Ref: Boris A. Kordemsky, Köpfchen muss man haben, 1975, P241
The Solution If you order the letters according there values you get a german word.

 ABC *   DC = EAEF
  *      +      -
  BF + AEGG = AEBF
------------------
FFEE + AEDC = DBHG

Ref: Torsten Sillke
The Solution

three solutions

  AB *   CD = EFCB
  *      +      -
  EC +  GBB =  GEC
------------------
EBDB +  GCD = EDBD

Ref: Torsten Sillke
The Solution

four solutions

 ABC *   BB = ADBC
  *      +      -
   E +  ACC =  ACE
------------------
FGEC +  ABB = ABCB

Ref: Torsten Sillke
The Solution

 ABC :    C =   DE
  -      *      +
  AE +   AF =   DD
------------------
 BGA -  FHC =   IJ

Ref: J. Petigk, Mathematik in der Freizeit, 1998, p151
The Solution

simple additions only
```
 A  +  B  =  CD
 +     +      +
CE  +  F  =  CF
---------------
CA  + CC  =  DE
```
Ref: J. Petigk, Mathematik in der Freizeit, 1998, p159
Note there was a printer error in the last line in the book where the wrong equation CG + CC = HE is given. Show that this modified problem has no solution. The Solution

additions and subtractions

 ABC - DBB  = EFG
  +     +      +
 ABB - ECC  = BBB
-----------------
DBEB - HBB  = IBC

Ref: Jürgen Köller, Symbolrätsel 2
The Solution

multiplication and division

  AB * BC  =  DAD
  *    :       *
  EC :  F  =    F
-----------------
 BCD *  G  = BBEA

Ref: Jürgen Köller, Symbolrätsel 4
The Solution

additions only

HJ  +  AD  =  DF
 +      +      +
BG  +  EC  =  DF
----------------
AC  +  GE  = HEK

Ref: Trend-Nüsse 1981, p52
The Solution

additions and subtractions

ISE + EID  = ALK
 -      +     -
RAS -  KL  = RUM
----------------
ERR + MDR  = LLM

Ref: Zeit Magazin 19/1972
The Solution

ABC - DEF  = EG
 +      -     :
HIE : DAH  =  H
---------------
FBD :  HB  = DF

Ref: Eckstein, Symbolrätsel, www.eckstein.de
The Solution

```
AB  +   C  =  AC
 +      +      +
AD  +   E  =  FB
----------------
FD  +   G  =  EC
```
Ref: W. N. Bolchowitinow, B. I. Koltowoi, I. K. Lagowski; Spass für freie Stunden, 1980, problem 194 A
Ref: J. Lehmann, Mathe mit Pfiff, Manz Verlag 1977, p72, problem 23
The Solution

AB  *   A  = CCD
 -      *      +
AE  :   F  =   G
----------------
 B  *  CF  = CHE

Ref: J. Lehmann, Mathe mit Pfiff, Manz Verlag 1977, p72, problem 25
The Solution

```
 E  *   K  =  BE
 +      *      :
 B  :   N  =   N
----------------
DN  +  DN  =  NB
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution
```
AB  *   C  =  CD
 -      +      :
 E  :   B  =   F
----------------
 F  +   G  =   H
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution
```
AB  *   C  = DEB
 +      +      -
AC  *   B  = FBB
----------------
GE  -  FE  =  CE
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution
```
AB  *   B  = CDD
 :      *      :
CB  :   B  =   E
----------------
 E  *   D  =  BD
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution
```
AB  *   C  =  DE
 *      +      -
 F  *   F  =  AC
----------------
GH  +  AI  =  CH
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution
```
ABB  :   C  =  DB
  *      +      -
  E  *   A  =   C
-----------------
 FC  :  GA  =   B
```
Ref: Walter Lietzmann, Lustiges und Merkwürdiges von Zahlen und Formen, 11.Ed, p192
The Solution

ABC :  CD  =   EF
 -     *       +
FDF +  EG  =  AHD
-----------------
 BB + FGA  =  AIJ

Ref: Bernhard Berchtold, www.mathematik.ch/puzzle/, Puzzle 9
The Solution

A  -  B  =  C
            *
D  :  E  =  F
            =
G  +  H  =  I

The Solution

magic cryptarithm
```
 VV  RE  HR
 AH  VE  RL
 RV  HE  VR
```
This is a magic square with magic constant HEH. If you order the letters according there values you get the hidden word.
Ref: Praxis der Mathematik 39:4 (1997) 153
The Solution
a bigger magic cryptarithm
```
 HG GH UF LI  U
 IF  I EU GG UH
 NU UG IH FF EI
 FH HF NI RU IG
 RI LU FG HH GF
```
This is a magic square with magic constant RHH. The 25 numbers form an arithmetic progression. If you order the letters according there values you get the hidden word.
Ref: Zweisteins Zahlenlogeleien, Insel it 1510, Problem 22
The Solution

Alphacipher

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

explain
```
161 + 134 + 145 = 503
```
Ref: Geoffrey Mott-Smith, Mathematical Puzzles, 1954, Problem 32
find the clue
```
R O M E  -  S U M  =  R U S E
```
Ref: Stephen Barr, Mathematical Brain Benders 2nd Miscellany of Puzzles, 1969, Problem 22

Sense

What SENSE does it make, if nine HENS give seven EGGS?

Author: J.A.H. Hunter

Cut

W E ) G E T ( I T
      W E
      ---
      C U T
      x x x
      =====

Author: J.A.H. Hunter

Printers Errors

2^5*9^2 = 2592
Ref: Dudeney, Amusements in Math, 1917, Problem 115, A printer's error, pp.20 & 162.
Ref: Hubert Phillips, Question Time, 1937, Problem 133, pp.87 & 219.
Ref: Donald L. Vanderpool, Printer's `errors', Rec Math Mag 10 (Aug 1962) p.38. (Some extensions)
Ref: Printers Errors - Eric W. Weisstein

Equation Puzzles

Equation Puzzles

Operator Puzzles

ascending order
```
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9  =  10
```
Replace the 'x' by '+', '-', '*', '/'. No operator occurrs more than twice. Evaluate left to right.
Ref: Zeit Magazin, Nr 13, 22. Mar. 96, Logelei

References

W. W. Rouse Ball
Mathematical Recreations and Essays, Dover publications, New York, 12. Edition 1974 (edited by H. S. M. Coxeter) Chapter I.8: Arithmetical Restoration (p20-26, 12 problems)
W. N. Bolchowitinow, B. I. Koltowoi, I. K. Lagowski
Spass für freie Stunden, Verlag für die Frau, Leipzig, 1980, 2. Auflage
(18 Cross Number Puzzles, 10 alphametic problems)
Maxey Brooke
150 Puzzles in Crypt-Arithmetic, Dover Publ. 1963, 72pp
(156 problems with great varity in type and level)
Pieter van Delft, Jack Botermans
Creative Puzzles of the World, (german: Denkspiele der Welt, Hugendubel, 1977)
(8 alphametic problems)
Angela Dunn
Mathematical Bafflers, Dover Publ. 1980, ISBN 0-486-23961-6
(3 alphametic problems)
Angela Fox Dunn
Second Book of Mathematical Bafflers, Dover Publ. 1983, ISBN 0-486-24352-4
(7 alphametic problems)
Jack van der Elsen
Alphametics, (Dutch), Shaker Publishing B.V. ISBN: 90-423-0084-1
60 pages
William A. Ewbank
Cryptarithms: Math Made Me Daft, Mama, Mathematics Teacher (Jan 1988) 54-60
Dick Hess
Puzzles from around the world, Apr. 1997, p37, distributed by the author,
Add: 4100 Palos Verdes Drive East, Rancho Palos Verdes, CA 90275-6462
Contains 4 alphametics and 3 cross number puzzles
P. Holzamer
Kreuzzahlenrätsel und Zahlenknobeleien, Harri Deutsch Verlag, 1994, Tb. Band 80, ISBN 3-8171-1321-8, 150p
Contains 178 alphametics and cross number puzzles.
J. A. H. Hunter
Mathematical Brain-Teasers, Dover Publ. 1976, ISBN 0-486-23347-2
Part: Alphametics (40 problems)
J. A. H. Hunter
Challenging Mathematical Teasers, Dover Publ. 1980, ISBN 0-486-23852-0
Part: Alphametics (p87-96, 40 problems)
J. A. H. Hunter
Entertaining Mathematical Teasers - and How to Solve Them, Dover Publ. 1983, ISBN 0-486-24500-4
Part: Alphametics (p87-100, 40 problems)
Steven Kahan
HAVE SOME SUMS TO SOLVE, the completest alphametics book, Baywood Publ. Company, Inc., Amityville, New York, ISBN 0-89503-007-1, 128p
(51 problems)
Steven Kahan
AT LAST!! ENCODED TOTALS SECOND ADDITION, Baywood Publ. Company, Inc., Amityville, New York, ISBN 0-89503-171-X, 138p
(42 problems)
Steven Kahan
TAKE A LOOK AT A GOOD BOOK, Baywood Publ. Company, Inc., Amityville, New York, ISBN 0-89503-142-6, 130p
(41 problems)
Donald E. Knuth
The Art of Computer Programming
Section 7.2.1.2: Generating all permutations. Zeroth printing (2002)
(20 problems)
Harry Langman
Play Mathematics, Hafner Publ. 1962
Chap. IV: Letter Division (49 problems)
Chap. V: Skeleton Division (24 problems)
Johannes Lehmann
Mathe mit Pfiff, Manz Verlag 1977, ISBN 3-7863-0383-5
Chap: Kryptarithmetik (p71-72, 29 problems)
Johannes Lehmann
Mathe mit Herz, Urania Verlag 1991, ISBN 3-332-00479-4, new edition of "Mathe mit Pfiff"
Chap: Kryptarithmetik (p81-83, 29 problems)
Walter Lietzmann
Lustiges und Merkwürdiges von Zahlen und Formen, Verlag Vandenhoeck & Ruprecht, Göttingen 1955, 8. Auflage, ISBN 3-525-39112-9
Chap II.5: Vergilbte Manuskripte (p128-131, 21 problems)
Chap II.13: Anagramme, Kryptogramme, Geheimschriften und dergleichen (p191-192, 10 problems)
Joseph S. Madachy
Madachy's Mathematical Recreations, Dover Publ. 1979, ISBN 0-486-23762-1
Chap. 7: Alphametics (p178-200, 37 problems)
Geoffrey Mott-Smith
Mathematical Puzzles - for beginners and enthusiasts, Dover Publ. 1954, 2nd Ed., ISBN 0-486-20198-8
Chap. 7: Properties of Digits (p67-78, 10 problems)
Randall K. Nichols (LANAKI)
Classical Cryptography Course (Vol I and II), Aegean Park Press, 1996-1997, 301 and 450pp., ISBN 0-89412-263-0 and 0-89412-264-9 respectively.
How to solve them. Lessons by LEDGE (Dr. Gerhard. D. Linz) in Vol I, chap. 8 and Vol II, chapt. 14 and 18.
Jürgen Petigk
Mathematik in der Freizeit, Aulis Verlag Deubner & Co, Köln, 1998, ISBN 3-7614-1997-X
Wir bauen ein Zahlenrätsel (p150-159)
Dr. Martin Sändig
Hobbymatik, Über 200 Symbolrätsel mit Lösungs- und Bastel-Tips,
Verlagsbuchhandlung Elmar Sändig, Walluf, 1984, ISBN 3-924395-01-2, 246p
over 200 problems, 100 with extended solution.
Zweistein
Zweisteins Zahlenlogeleien, Insel Tb. 1510, 1993, ISBN 3-458-33210-3, 100p
Contains alphametics (40 problems) and cross number puzzles only
N. V. Findler, P. Bunting
Some Ideas about the Solution of Cryptarithms, Journal of Recreational Puzzles 7:4 (1974) 309-14
An alphametics solver
Journal of Recreational Puzzles
Each issue contains several Alphametics.
Zeit Magazin
Section 'Logelei' contains now and than an alphametic.
Usenet
alphametic articles found in rec.puzzles.

Alphametic and Cryptarithms Links

Cryptarithms Online
www.geocities.com/Athens/Agora/2160/ - Jorge A. C. B. Soares, contains the Sphinx Collection, Link, Books
An Alphametic Page
Truman Collins' alphametic page - he has solvers and even generators
An Alphametic Page
Mike Keith's alphametic fan page . A must for alphametic lovers. (local copy)
A Cryptarithms Page
http://eureka.vermontel.com/~kms/Cryptarithms.html
A Cryptarithms Page
http://www.geocities.com/Colosseum/Stadium/5002/Cryptarithms.html - Diogenes. Large collection of Cryptarithms
An Alphametic Page
http://www.contestcen.com/rithms.htm and http://www.contestcen.com/rithm2.htm - Frank Rubins's alphametic pages contain large sums
Solving Word Arithmetics www.jimloy.com/puzz/wordarit.htm - Jim Loy explains how to solve long division problems
Prime Alphametics www.primepuzzle.net/puzzles/puzz_179.htm - double true and magic square alphametics using prime numbers
A Cryptarithms Page
www.cut-the-knot.com/cryptarithms/st_crypto.html - Alexander Bogomolny
A Cross Number Puzzles Page
home.t-online.de/home/nagel.klaus/knodir/zahl.htm - Klaus Nagel, Applet to generate these puzzles.

Cryptarithms Programs

Truman Collins
http://www.tkcs-collins.com/truman/alphamet/alpha_solve.shtml and http://www.tkcs-collins.com/truman/alphamet/alpha_gen.shtml
Eldad
http://www.Elemental.co.il/~eldad/
kms
http://eureka.vermontel.com/~kms/vrsion21.zip
Robert Israel
Maple Program
comp.sources.games
comp.sources.games/volume5/crypto.Z

Torsten Sillke

Home | FSP Mathematisierung | Fakultät für Mathematik | Universität Bielefeld

Last Update: 2005-12-24