The Square Root of Passion

heart equation

In the novel City of Angels (1975), Steve Shagan wrote, “But you can’t make arithmetic out of passion. Passion has no square root.” However, puzzlist Alan Wayne countered, “On the contrary, one can show that the alphametic


has a unique solution.”

Was Wayne correct? Can you find the unique solution in base 10? That is, find the unique digits (0 – 9) representing the letters P, A, S, I, O, N, and K such that the equation holds.

Solution (Click to Show)

As PASSION has seven letters, this means that it corresponds to seven digits, we know that KISS < $latex \sqrt {10,000,000} ≈ 3,162. Therefore, K is either 1, 2 or 3 and if K is 3 then, we can say that I ≤ 1. S has to be either 2, 3, 4, 7 or 9 since PASSION doesn’t end in S. Note that S is eliminated as 88 × 88 = 7,744. Now, since SS² ends in ON and ISS² ends in ION, we can make a summary of possibilities:

19 02 13 22 58 33

From the choices, only KISS = 2,033 satisfies the alphametic equation:

\sqrt {4,133,089}=2,033


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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is

10 thoughts on “The Square Root of Passion

  1. After pondering your initial equation which, in English, might be that (at) the Root of Passion is a Kiss, I was going to say therefore a KISS squared = PASSION (which is like saying lots of Kisses is the equivalent of Passion). It’s all quite logical really. 🙂
    (However, and sorry to be pedantic but, I then noticed that your last equation said the root of 4133089 = 2033 squared, which I presume is a typo).

    Liked by 1 person

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