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25th June 2020

I've recently been working on improving the word games on Pencil and Paper Games, and while testing Word Ladders I happened to get a particularly hard ladder; you might like to try it:


Theoretically, the shortest possible ladder with four-letter words, and no matching letters, is 5 steps. How close can you get to this?

Hardest four-letter ladder

After finding this ladder I wondered whether I could search for the hardest possible four-letter ladder; in other words, the pair of words that requires the largest number of steps. My first attempt at writing a program to do this, using the PAPG word database, was going to take something like 4000 hours to check all possible ladders, which didn't seem feasible.

After making a few assumptions to reduce the number of words I was testing I managed to get this down to under an hour.

Here's the nicest maximal word ladder I found:


If only AMEW or ANEN were valid words it would be possible to solve this in a three-step ladder. I warn you: this is a hard one! However, none of the words in the ladder are obscure.

Hardest three-letter ladder

If you want to warm up on something a lot easier, here's one of the longest word ladders I found with three-letter words:


The answers

Here are the answers:

anew to amen – 17 steps:

anew knew know snow show shod shed seed deed dyed dyes eyes eves even oven omen amen

ivy to end – 8 steps:

ivy icy ice ace act ant and end

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