w1 < w2
if every letter of w1 occurs earlier in the alphabet than the corresponding letter of w2. For example, we write
ACE < PYX
because A is earlier in the alphabet than P, C is earlier in the alphabet than Y, and E is earlier in the alphabet than X.
There exist words "between" ACE and PYX. For example,
ACE < EON < PYX
as you can check. A solution to the Alphabet Slider is a chain like the one above, and the goal is to find the longest possible chain. With the help of a computer, I found this solution:
ACE < BEG < CHI < DIM < EON < FRO < ITS < JUT < PYX.
(An equally long chain results from using NUT instead of JUT. A reader also notes that OUT could go in this position.)
The game can be played with words of any length. For example, here's a pretty good chain of four-letter words:
ABBE < DILL < ELMS < FONT < GROW < JURY.
For eight-letter words, I found
HEADACHE > KNEELING > SPONSORS.