# Triple up, pair off, and single out

Can you transform this word triple

PELTS  SORES  DIVAN


into this word triple

PLOTS  DIVES  SANER


just by swapping pairs of letters?

You may swap any pair of letters you like, either between two words (e.g., TRIES and NODES can swap the "T" and the "D" to become DRIES and NOTES) or within the same word (e.g., MODES can swap its own "M" with its own "D" to become DOMES). However, after each swap, we should see a triple of English words.

Inevitably with this kind of puzzle, the question comes, "What exactly constitutes an English word? Which word list or dictionary should we use?" There is at least one solution to this puzzle using very common words, and at least one solution incorporating more obscure words. Either solution is acceptable, but you are encouraged toward the more common words because it is more fun for everyone.

Also acceptable are widely-used proper nouns and adjectives, such as DUTCH, DANES, SLAVS, and WELSH.

Bravo to @AxiomaticSystem for finding such a concise solution!

I have also presented an alternative solution using only the most common words for those who might be pursuing that path. It's not nearly as succinct.

• Must the words in the triple end up in the given order? e.g. would a solution leading to PLOTS SANER DIVES work? May 23, 2022 at 19:55
• river-crossing? May 23, 2022 at 20:03
• @bobble – The words in the final triple must appear exactly as presented, so PLOTS DIVES SANER only. Consider it to be three words in a single string and you are performing a string transformation in a series of steps. May 23, 2022 at 20:04
• @RobPratt – Yes, because you starting at one state and trying to cross to another state through a series of steps, some of which might appear like going backward. (In a way, it's also a maze, in the sense of navigating the graph of states.) May 23, 2022 at 20:09
• Fascinating puzzle! May 24, 2022 at 0:24

I can do so in fifteen transpositions:

For accessibility:

Pelts Sores Divan
Pests Lores Divan
Pests Loser Divan
Pests Loner Divas
Pasts Loner Dives
Pasts Liner Doves
Pasts Lined Roves
Pasts Lines Roved
Lasts Pines Roved
Salts Pines Roved
Slats Pines Roved
Slots Pines Raved
Plots Sines Raved
Plots Dines Raves
Plots Dines Saver
Plots Dives Saner

Alternative solution which uses only the most common words:

PELTS SORES DIVAN
PELTS ROSES DIVAN
PESTS ROLES DIVAN
RESTS POLES DIVAN
RENTS POLES DIVAS
RANTS POLES DIVES
PANTS ROLES DIVES
PANTS SOLES DIVER
PANTS LOSES DIVER
PANTS DOSES LIVER
PANTS ROSES LIVED
PANTS SORES LIVED
PANES SORTS LIVED
PAVES SORTS LINED
SAVES PORTS LINED
SAVED PORTS LINES
RAVED POSTS LINES
ROVED PASTS LINES
ROVED LASTS PINES
ROVED SALTS PINES
ROVED SLATS PINES
ROVED SLAPS TINES
ROVED SNAPS TILES
LOVED SNAPS TIRES
LOVED SPANS TIRES
LOVED SPANS RITES
LOVED SPINS RATES
LOVER SPINS DATES
LOVER SPITS DANES
LOVER SPATS DINES
LOVES SPATS DINER
DOVES SPATS LINER
DIVES SPATS LONER
DINES SPATS LOVER
DANES SPITS LOVER
DATES SPINS LOVER
RATES SPINS LOVED
RITES SPANS LOVED
TIRES SPANS LOVED
TILES SPANS ROVED
TILES SNAPS ROVED
TINES SLAPS ROVED
PINES SLATS ROVED
PINES SALTS ROVED
PINES LASTS ROVED
LINES PASTS ROVED
LINES POSTS RAVED
LINED POSTS RAVES
LINED PORTS SAVES
LINED SORTS PAVES
LIVED SORTS PANES
LIVED SORES PANTS
LIVED ROSES PANTS
LIVER DOSES PANTS
DIVER LOSES PANTS
DIVES LOSER PANTS
DIVES LONER PASTS
DOVES LINER PASTS
LOVES DINER PASTS
LOVER DINES PASTS
LONER DIVES PASTS
LOSER DIVES PANTS
LOSES DIVER PANTS
DOSES LIVER PANTS
ROSES LIVED PANTS
SORES LIVED PANTS
SORTS LIVED PANES
SORTS LINED PAVES
PORTS LINED SAVES
POSTS LINED RAVES
POSTS LINES RAVED
PASTS LINES ROVED
LASTS PINES ROVED
SALTS PINES ROVED
SLATS PINES ROVED
SLAPS TINES ROVED
SNAPS TILES ROVED
SNAPS TIRES LOVED
SPANS TIRES LOVED
SPANS RITES LOVED
SPINS RATES LOVED
SPINS DATES LOVER
SPITS DANES LOVER
SPATS DINES LOVER
SPATS DIVES LONER
SPATS DOVES LINER
SPATS LOVES DINER
SPATS LOVER DINES
SPITS LOVER DANES
SPOTS LIVER DANES
SPOTS DIVER LANES
SLOTS DIVER PANES
SLOTS DINER PAVES
PLOTS DINER SAVES
PLOTS DINES SAVER
PLOTS DIVES SANER