# Creating Equation Haikus using Constraint Programming

Bob Bosch pointed out (in a response to Shea Serrano, wonderfully…) that 77 + 123 = 200 is a haiku in English:

How many such haikus are there? Well, we can use constraint satisfaction (CSP) to give us an idea (Python code here for the impatient):

A traditional haiku consists of three lines: the first line has five syllables, the second seven, and the last five, for a total of seventeen syllables.

We can write equations that describe our problem. First, let’s define the function s[n] as the number of syllables in the English words for n. For example, s = 7; try saying “eight hundred seventy four” out loud. It’s not that hard in English to compute s[n]; at least, I don’t think I messed it up.

Let’s call A the number in the first line of the haiku, B the second, and C the third. If we want a haiku with the right number of syllables and for the equation it describes to hold, all we need is:

s[A] = 5
1 + s[B] = 7 (since “plus” is one syllable)
2 + s[C] = 5 (since “equals” is two syllables)
A + B = C

If you let A=77, B=123, C=200 as in Bob’s example, you will see the above equations hold.

Using the constraint package in Python, it’s easy to create this model and solve it. Here is the code. A great thing about CSP solvers is that they will not just give you one of the solutions to the model, but all the solutions, at least for cases where A, B, C <= 9999. It turns out there are 279 such haikus, including

eight thousand nineteen
plus nine hundred eighty one
equals nine thousand

and the equally evocative

one hundred fourteen
plus one hundred eighty six
equals three hundred

Of course, this is not the only possible form for an equation haiku. For example, why not:

A
+ B + C
= D

I invite you to modify the code and find other types of equation haikus!  