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


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

• 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. – Gareth McCaughan Jan 13 '19 at 20:42
• ...Ah, so I do! – Jonathan Allan Jan 13 '19 at 20:43
• Added the missing entry. – Jonathan Allan Jan 13 '19 at 20:45
• 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 :-). – Gareth McCaughan Jan 13 '19 at 20:46