Thursday, April 21, 2016

Directional Change-A-Word

Inspired by reader mdahlman's comment on the Alphabet Slider puzzle, I came up with this variation on the traditional "Change-A-Word" puzzle:

BAA

WRY
Change one letter at a time until BAA becomes WRY. Each intermediate step must be a valid word. You may only change a letter into one that occurs later in the alphabet. 
I was able to do this in four steps. Can it be done in three?

At the other extreme, the most meandering solution that I could find has 31 steps. (I found it using a computer.) I'll share it next time.

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Some notes:

(1) This game isn't equivalent to the one mdahlman had in mind, because only one letter at a time can change.

(2) A long time ago, I reported that in the standard Change-A-Word game, most four-letter words can be reached from most four-letter words. Four-letter words are like a vast, connected raft, or continent, with just a few isolated offshore islands. Here's the largest of the islands:


In a comment on that post, reader danimal suggested a variation on Change-A-Word in which the player may only change a given letter to a letter adjacent to it in the alphabet. I found it difficult to create instances of that version of the game, but the upshot of the present post is that we get plenty of instances if we replace the adjacency requirement with a directional requirement.

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