# Arithm’ and clues in Puzzlebomb

I had my second puzzle in the January 2015 online puzzle sheet Puzzlebomb, entitled “Arithm’ and clues“. It’s a series of cryptarithm puzzles with the same letters denoting the same numbers throughout, but with none of the words given: instead they’re clued. It’s like a crossword but with arithmetic replacing the grid.

Go on and give it a try before reading on, as there are some tiny hints ahead.

Typically, a satisfying cryptarithm, or alphametic, will also ‘make sense’. For instance, the most famous, and for me the most memorable, is:

I tried to emulate this as far as possible,  though it’s hard to come up with something quite as satisfying. The solution to “Chuck+Changed=Deleted”, when read one way, is my favourite.  To design the puzzle: I fixed the letters to use, randomly assigned some numbers to them, and wrote a Python program to run through a decently conservative word-list checking for sums and multiplications that worked. I did this a few times, looking through for a good set of common words, and then started whittling it down to give me a set of puzzles which, when combined, gave a unique solution. The shortlist was further culled for other reasons: one was slightly more morbid and shorter than I wanted [1]; other words were pretty unclueable [2] using the brief, straightforward, single word clues I’ve gone for (apart from the more elliptic “Past-botherer” clue.)

There’s plenty more scope for other puzzles in this same style, in contast to my previous Puzzlebomb submission “In Their Prime“, which was pretty much a one off-puzzle. There’s also plenty more scope for clever individual cryptarithms that make internal sense than are available to traditional cryptarithms. This is because each individual sum no longer requires a unique solution, and without this restriction, there’s simply more of them. However you also need to find more such word sums.

I’m not sure what inspired this puzzle (possibly something at the 2014 MathsJam conference?). Whereas “In Their Prime” was a deliberate attempt to use the idea of studying inheritance of hereditary diseases in family trees, this idea somehow popped into my head fully formed. It’s certainly possible something similar may have been done elsewhere before, but I haven’t knowingly seen it.

Obviously, the English words and clues mean this puzzle isn’t as universal as “In their prime” (which did get translated onto a Spanish puzzle site at one point). I realise some people dislike wordier puzzles or find them harder, but I hope the fact that you can go back and forth between the sums and the clues (with a reduced set of letters) to work things out, makes it a bit more palatable to these folk. In fact, like the SEND + MORE = MONEY puzzle, you can deduce at least a few numbers without using any of the word clues; or you can use crossword clue logic to make some educated guesses about the word endings [3] And there is one additional hidden cryptic meta-hint lurking about if you need it.

Many thanks to the Puzzlebomb team for all their prettification and editorial contributions, and to several MathsJam guinea-pigs who I originally presented this puzzle to without any instructions (and solved it).

If you want some traditional cryptarithms, or to learn a bit more about them, Jorge Soares‘ site seems like a good place to start looking.

1. IN + END = DIE
2. DEIST
3. For instance in the aforementioned “Chuck + Changed = Deleted”.