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We are going to construct word ladders, but unlike the classic word ladders in which only one letter can change per step, you may change as many letters as you like at each step. However, each letter can only move up or down one click in the alphabet.

For example, BOOMERS changes to COOLEST in a single step. (The B moves down to a C, the first O doesn't change, the second O doesn't change, the M moves up to an L, the E doesn't change, the R moves down to an S, and the S moves down to a T.)

For added fun, let's agree that A can move "up" to Z, and Z can move "down" to A. In other words, the alphabet forms a wheel. This might remind you of a bike lock, with alphabetical wheels in place of numerical wheels.

Let's walk through an example.

Go from PUTTING to PURRING in three steps:

start:   PUTTING
step 1:  OUSTING
step 2:  PURSING
step 3:  PURRING

Obviously, each intermediate step must also form a known word.

See if you can solve these:

1.  Go from ACTRESS to BARTERS in five steps or fewer

2.  Go from SKINLESS to SKILLETS in five steps or fewer

3.  Go from DONNING to BONKING in six steps or fewer

4.  Go from EARNEST to HAULERS in nine steps or fewer
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  1. Four steps:

 ACTRESS
 ABUSERS
 BATTERS
 BASTERS
 BARTERS

  1. Three steps:

 SKINLESS
 SLIMMERS
 SLIMMEST
 SKILLETS

  1. Three steps:

 DONNING
 DOOMING
 COOLING
 BONKING

  1. Four steps:

 EARNEST
 FARMERS
 GASLESS
 HATLESS
 HAULERS

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  • $\begingroup$ Drat! The last one was giving me grief. Nicely done! But you need one more step for #1. [EDITED to add:] JA has fixed #1 now. $\endgroup$ – Gareth McCaughan Jan 13 at 20:42
  • $\begingroup$ ...Ah, so I do! $\endgroup$ – Jonathan Allan Jan 13 at 20:43
  • $\begingroup$ Added the missing entry. $\endgroup$ – Jonathan Allan Jan 13 at 20:45
  • $\begingroup$ I had the same solution as you (after the correction) for #1, and for #3, but an entirely different route for #2. I'd had hopes that we could get DOMMING into the solution aiming toward BONKING, but wasn't able to make that happen :-). $\endgroup$ – Gareth McCaughan Jan 13 at 20:46

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