Fun with Algebra

This is a guest post by Danielle Brooksis, a regular contributor on If you want to write a guest post, get in touch at vineetpatawari[at]gmail[dot]com.

Algebraic Equations for Fun!

There was a lot of positive feedback about the alphametic cryptatrithms, I posted a few months ago: so here is a little game that is based on the same idea, but with a different execution. This version is fun for those with a propensity towards algebra, and geared more toward middle school or high-school ages; however, if you are an adult, please enjoy them as well. There are a few less steps here than in the cryptarithms, but I’m sure y’all will get a kick out of them all the same!

  1. (DD)^E  = DEED

First, identify what you know. D=D and E=E. The sum is four digits. If we begin our trial and error and start with the numeral 1, we can infer that (11)E  = 1EE1. Now, to find E: We know that it can’t be 1, since D=1. 112 = 121. But, 113 = 1331. There is the answer!

You can utilize a few math tricks here to eliminate some of the trial and error. Call upon old favorites like the square root trick, and don’t be fooled by simple mistakes (anything multiplied by 0 is 0!).

Here is another one:


I’ll let you work your way through this one. Here are some more for you to work through and if you solve all of them, you can find more at


Solve them all? Try writing one yourself and share it.

1.         CAT = (C + A + T) × C × A × T

 2.         ABC × DEF = 123456, if A = 1

 3.         CL=LOGIC

 4.         COW × COW = DEDCOW

Answers to the problems can be found on the link above.

Author Bio: As a law student, Danielle often uses conference call technology to attend virtual networking events, as well as to interview professionals in her field about case studies for homework. Visit her blog,, to read about student-friendly technology and innovation.

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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 “Fun with Algebra”

  1. I have some doubt

    (11) power 3 i.e. 11x11x11=1331 (based on your formula (11)E = 1EE1

    But in case of (11)power 4 i.e. (11)4=11x11x11x11 144441 (i.e. here e=4)

    ABCD x D = DCBA
    1089 x 9 = 9801 but it is applicable only for 1089 not for other numbers.

  2. ABCD x D = DCBA
    1089 x 9 = 9801

    1. CAT = (C + A + T) × C × A × T
    135 = (1+3+5) x 1x3x5

    2. ABC × DEF = 123456, if A = 1
    192 x 643 = 123456

    3. CL=LOGIC
    ??? – not sure what this is supposed to mean.

    4. COW × COW = DEDCOW
    376 x 376 = 141376

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