Sunday, April 24, 2016

BAA to WRY in 32 Steps

In this post, I'll show the promised long chain from BAA to WRY. To make contact with where we began, I'll recast the problem as an Alphabet Slider.


Right now, the sliders indicate the word BAA. If you move the sliders down far enough, you can indicate the word WRY.

So here's the game: how many words can you form by moving sliders downward? The game is over when the sliders finally indicate WRY.

Note, on each play, exactly one slider moves down.

(For the answer I found using a computer, scroll down.)




























BAA
BAD
BAG
BAH
BAM
BAN
CAN
CAP
CAR
EAR
FAR
GAR
GAS
HAS
HAT
HAW (fruit of a hawthorn)
JAW
LAW
LAX 
LAY
MAY
NAY
PAY
RAY
SAY
SHY
SKY
SLY
SOY
TOY
TRY
WRY

This solution leaves the central A in place for a very long time, eventually harvesting a run of six -AY words before finally taking advantage of the possibilities afforded by the initial letter S to branch out at the middle position.

Here's what the endgame looks like as a graph. Each vertex is a word, and an arrow points from one vertex to another if it is a fair play to change the first word into the second. (I removed direct shortcuts from the graph.) Sorry the word labels aren't visible—LAX is at the top, and TRY is at the bottom.






2 comments:

Sue Thuma said...

In your computer list CAM should be CAN

Jason Zimba said...

Thanks Sue! Fixed.

I think what happened is that two paths are possible at this junction (BAM/CAM/CAN or BAM/BAN/CAN) and I accidentally blended the two.