Alphametic Cryptarithms

This is a guest post by Danielle Brooksis

Alphametic = Alphabets + Arithmetic

Alphametic cryptarithms are a fun way to bridge the gap between math and language, particularly good for training young people to think logically and use reasoning.

Wikipedia definition: Verbal arithmetic, also known as alphametics, cryptarithmetic, crypt-arithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters.

I like to pass time figuring out math puzzles, because there is no ONLINE ANSWER SERVICE for them. Louis Sachar has written a series of children’s books based on the fictional elementary school Wayside. The fifth novel in the series introduces readers to a special type of “word math.” In an alphametic, each letter represents a number between 0 and 9. These puzzles usually put letters into an equation that forms words or phrases. Here is an example pulled from the book:

Example 1:

ELF

+     ELF

FOOL

E = ?                L = ?                O = ?                F = ?

Solving requires a series of deductions and a little bit of trial and error. The key here is to understand basic arithmetic. For this problem, once you solve for F, everything else falls into place. For example,

• In column four, F=1, because that’s the only possible carry from two single digit numbers
• In column one, the two Fs added together equals L or 2.
• In column two, the two Ls added together equals O or 4
• In column three, we know that the sum is 14 (F = 1, O = 4), and so E is a value that, added to itself, equals 14. Therefore E = 7

That was easy, but it was also intended for children. Here’s H.E. Dudeney’s classic example:

Example 2:

SEND

+       MORE

MONEY

Once again, in column five, M = 1 because it is the only possible carry.  Can you figure out the rest? You can find many alphametics to solve in your spare time on the internet. Here are some fun ones from http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/

What is the sum?

1.         E A R T H  +  A I R  +  F I R E  +  W A T E R

=          N A T U R E

2.

G A U S S

+ R I E S E

———–

E U K L I D

3.

F I V E

F I V E

N I N E

E L E V E N

————–

T H I R T Y

What is the product?

4.  H E  *  H E  =  S H E

5.  T H I S  *  I S  =  A P H I S

If you solve all these, try writing one yourself! If you want to play a little game based on the same idea, visit – Fun with Algebra

Author Bio: Danielle Brooksis a freelance writer currently studying business litigation. When not solving number puzzles she enjoys Terry Gilliam films, Scrabble and experimenting with soufflé recipes.

Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

5 thoughts to “Alphametic Cryptarithms”

1. Iamature says:

I did not understand these problems at all..Is there any detailed explanation for this?

2. Pingback: Fun with Algebra
3. Sidharth says:

In the first example why not L=3 , O=6 AND E=8….

4. ani says:

i really like this but can u tell in some more simpler manner