I went to one of those discovery stores and picked up a few Newton's cradles, except these have hanging words instead of hanging spheres.

Check it out:

This one has a starter pendulum with two letters instead of one:

And this big one has a starter pendulum with three lett...

Oh, shoot! I dropped it!!

Aw, geez, it broke apart and words are scattered everywhere... And the three little starter letters rolled under the stove. I guess we'll never see those again!

Can you help me reconstruct it?

I've gathered up the words from the floor. Here they are in no particular order:

COMMENTERS

DEFECATING

FEATHERBED

LASCIVIOUS

REORIENTED

RESILIENCY

UNDEFEATED

VEGETABLES

WATERLINES

WOMANIZING


Apology to the Brits: While recognizing that Newton was British, I used American spellings even so. You can expect "—IZING" instead of "—ISING", for example.

• Newton's own writings appear to use -ize as well as -ise. – Gareth McCaughan Jul 30 '19 at 18:44
• Is it allowed for a letter to be replaced by the same letter at the same position? – Arnaud Mortier Jul 30 '19 at 19:44
• @ArnaudMortier — As the letter group travels from one word to the next, it is certainly possible for them to maintain their relative positions in the word. For a double example, look above and see that "V" and "I" are the first and fourth letters of the word VARIATIONS, and then become the first and fourth letters of the word VISIBILITY. In that case, both letters maintain their respective positions in the word. No problem there. – SlowMagic Jul 30 '19 at 20:09
• However, it doesn't make sense to me for a letter to replace the same letter. If the traveling letter group is a trio, I would think that means three letters in the target word are going to be replaced by three different letters. Another way to say it: three letters in each word must change. – SlowMagic Jul 30 '19 at 20:09

Starter letters SLT

WATERLINES becomes SATELLITES, giving WRN

VEGETABLES becomes RENEWABLES, giving VGT

DEFECATING becomes VEGETATING, giving DFC

RESILIENCY becomes DEFICIENCY, giving RSL

UNDEFEATED becomes UNRELEASED, giving DFT

LASCIVIOUS becomes FASTIDIOUS, giving LCV

WOMANIZING becomes VOCALIZING, giving WMN

FEATHERBED becomes WEATHERMEN, giving FBD

REORIENTED becomes BEFRIENDED, giving ROT

COMMENTERS becomes TORMENTORS, giving CME as the final three letters

Some notes on my working (entirely trial and error):

FEATHERBED --> WEATHERMEN came first, since I didn't think much could change in this word and remain a legal word. I got quite fixated on this having to be correct, so was very pleased when I spotted that the resulting BFD led to changing REORIENTED to BEFRIENDED. The TOR providing me with the change from COMMENTERS to TORMENTORS came next, though it took a while longer to spot this. This left me with a CME I was struggling to substitute into another word...

Then:

The WMN to enable the FEATHERBED change had to come from WOMANIZING. What else could legitimately make a word of the pattern _O_A_IZING? Well, once I spotted FASTIDIOUS --> LASCIVIOUS, the resulting VCL neatly enabled VOCALIZING. How to get the FTD to enable this? Well, that had to come from either FEATHERBED (impossible), DEFECATING or UNDEFEATED. I could not be sure yet.

Another pairing which seemed nicely matched was a possible change from RESILIENCY to DEFICIENCY, freeing up RSL. To do this required the DFC from DEFECATING, giving a word of the form _E_E_ATING. This also meant that FEATHERBED's FTD had to come from UNDEFEATED, giving a word of the form UN_E_EA_ED or UNDE_EA_E_.

Next:

I turned my attention to VEGETABLES. There are not many words which begin with VEGE or contain EGE, in my experience. This meant that likely the V and/or G would have to change. Since the ABLES suffix is fairly common, I concentrated on words of the form _E_E_ABLES. This freed up a VGT to create VEGETATING as the step before DEFECATING. What could go in the gaps? After several failed attempts looking for letters available in unused words I hit upon RENEWABLES, using the RNW from WATERLINES.

So what could WATERLINES become without RNW? Something of the form _ATE_LI_ES... I entertained the possibility of SATELLITES as one option, but the required SLT was not available in another word...

This left me two 'chunks':

WATERLINES + SLT --> SATELLITES + RNW
VEGETABLES + RNW --> RENEWABLES + VGT
DEFECATING + VGT --> VEGETATING + DFC
RESILIENCY + DFC --> DEFICIENCY + RSL

UNDEFEATED + ??? --> UN?E?EA?ED or UNDE?EA?E? + DFT
LASCIVIOUS + DFT --> FASTIDIOUS + LCV
WOMANIZING + VCL --> VOCALIZING + WMN
FEATHERBED + WMN --> WEATHERMEN + FBD
REORIENTED + FBD --> BEFRIENDED + ROT
COMMENTERS + ROT --> TORMENTORS + CME

Finally:

I tried to spot a connection between these two chunks for AAAAGES, teetering on the verge of adding UNRESEALED into the dictionary. Some minutes later, the facepalm moment struck: UNRELEASED! So the starter letters had to be SLT and the leftovers CME.

Phew! Definitely time for bed...

• Funny I got the same starting point as you - but you beat me to a complete solution. – Arnaud Mortier Jul 31 '19 at 10:08
• Impressive! Looking at the question I was in some doubt as to whether it was solvable by human brains at all without an excessive amount of work... – Gareth McCaughan Jul 31 '19 at 11:07
• @GarethMcCaughan Thanks. It took me probably 1h15 of solid thought in the wee hours of the night when I probably should have been sleeping. I'm sure some might call that excessive! :) – Stiv Jul 31 '19 at 11:11