Sunday, 8 March 2015

Cryptarithmetic problem

Cryptarithmetic problem is a type of mathematical game consisting of arithmetic operations among unknown numbers, whose digits are represented by alphabets. It is generally a number puzzle problem in which a group of arithmetic operations has some or all of its digits replaced by alphabets or symbols (for example, if Z=4, then ZZ=44), and where the original digits must be found [1]. In such a problem, each alphabet or symbol represents a unique digit and arithmetic operations might be addition, multiplication or division.  
Example:
     EAT
+THAT
APPLE
Here we know that T is not 0, as T+T is not equal to T. The case is same with A. After that we have to solve every letter for the problem making each letter unique. The steps are below.
     EA9
+9HA9
APPLE

     8A9
+9HA9
APPL8



     819
+9H19
APPL8

     819
+9H19
APP38

    819
+9219
A0038

    819
+9219
10038

FINAL ANSWER:
EAT = 819, THAT = 9219, APPLE =10038
Reference:

[1] E. Weisstein (2014). Cryptarithmetic. [Online] Available: http://mathworld.wolfram.com/Cryptarithmetic.html

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