Cracking the Code: A Journey into Cryptarithmetic Puzzles

 

A Puzzle That Teaches More Than Math  

“We use alphabets and digits throughout our life and so as Cryptarithmetic.”

                                                                                      -       Hitesh T. Jain

Cryptarithmetic(Alphametics) is the science and art of creating and solving Cryptarithms.

"If we want students who can think computationally, we must give them problems worth computing. Cryptarithmetic is precisely such a problem."

— Prof. S. Papert, Constructivist Learning Theory

Cryptarithm is a mathematical puzzle or riddle in which the digits are replaced by letters of the alphabet or other symbols. In a typical puzzle, there is a one-to-one correspondence between the numbers and the letters or symbols replacing them, i.e. the same digit is always represented by the same letter or symbol. The objective of the puzzle is to break the code used. That is, to replace each letter of the Cryptarithm by a numeral so that the resulting mathematical expression is true.

     


C: Cleverness required to crack the code.

R: Reasoning that guides us on the road.

Y: Wh(y) that makes us wonder.

P: Patience that we need.

T: Thrill that we feel when we succeed.

A: Arithmetic that forms the puzzle's seed.

R: Reward that we get from solving it.

I: Interest that keeps us from quitting.

T: Time that we spend on every clue.

H: Happiness that comes when we are through.

M: Magic that makes letters into numbers.

E: Elegance that sometimes makes us wonder.

T: Talent that we develop along the way.

I: Intuition developed throughout the journey.

C: Challenge that we always enjoy.


What is so intriguing about Cryptarithmetic? The answer to this question lies in the manner our formal education progresses. As a child, what are the first few things you learn? The alphabets A to Z and the numbers 0-9. Everything we learn throughout our life is based on these fundamentals (alphabets and numbers). We use these alphabets and numbers innumerable times throughout the day. Think if we were to interchange them. What if you had to use alphabets in place of numbers? You know all the mathematical operators but how do you use them to find out the value of each alphabet. What makes it more interesting is, it is possible to form puzzles using your name, place or any phrase of your choice. Though it is very time consuming to form the puzzle but it is full of fun and surprises.

 These puzzles are attracting and if anybody go through these puzzles then it is very difficult for him or her to quit it without solving. Solutions of these puzzles rarely require more than a sound knowledge and understanding of the basic of simple arithmetic, coupled with sound reasoning and often some patience.


The world's best known Cryptarithmetic puzzle is undoubtedly:

 


 

It was created by H. E. Dudeney and first published in the July 1924 issue of Strand Magazine associated with the story of a kidnapper's ransom demand.

Why Cryptarithmetic:

§ This is the best way to start programming.

§  This is also a part of Artificial Intelligence (AI).

§  It helps in developing child’s multiple dimensions thinking and problem solving skill.

§  This is part of almost all the competitive and scholarship exams like VVM, CAT, GATE, GRE, e-Litmus, CSAT, IPMAT, CUET etc.

 

Rules for solving the Cryptarithm

1.         All the letters or symbols are distinct from 0 to 9 i.e. no 2 letters can take same values.

2.         Each letter or symbol represents same digit throughout the puzzle.

3.         In any row, left most digit cannot be 0.

4.         When letters or symbols are replaced by respective digits, the resultant arithmetical operator must be true.

5.         Consider decimal number system (base 10), unless nothing is specified.

6.         There must be only unique solution, unless it is specified.

         (A truly elegant Cryptarithm should have a unique solution.).


Special puzzles 

1.     BHARAT MATA KI JAY

B

H

A

 

2

1

0

 

B and R can be

interchanged

R

A

T

3

0

6

 

+

M

A

+

8

0

 

 

T

A

 

6

0

 

 

K

I

 

4

9

 

J

A

Y

7

0

5

 

 

2.         FATHER OF ISRO: SARABHAI

 

 

S

A

R

A

 

 

3

5

4

5

 

B

H

A

I

 

2

8

5

9

+

I

S

R

O

+

9

3

4

6

J

A

N

A

K

1

5

7

5

0

 

3.         NOBLE WINNER  : CV RAMAN

 

 

R

A

M

A

N

 

 

4

2

9

2

6

 M and B can be   interchanged

+

N

O

B

L

E

+

6

3

7

5

8

W

I

N

N

E

R

1

0

6

6

8

4

 

4.     FATHER OF RELATIVITY: ALBERT EINSTEIN

 

 

A

L

B

 

 

 

3

9

4

B and T can be interchanged

 

 

E

R

T

 

 

7

8

6

+

R

E

L

A

+

8

7

9

3

 

T

I

V

E

 

6

0

2

7

 

 

E

I

N

 

 

7

0

5

S

T

E

I

N

1

6

7

0

5

 

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