Pass the Pair

Two letters go in, two different letters come out.

You’ll be given a starting pair of letters and a list of words. At each step:

  1. Insert the pair somewhere inside the next word — as a contiguous chunk — so that the result is a new word.
  2. Pull out a different two-letter slice of that new word, such that what remains is also a word.
  3. The slice you pulled out is the pair you insert into the next word. Repeat.

So every word you build splits two ways: undo the insertion and you get the word you started from; make the other cut and you get a word you throw away.

A quick example of one step: given RI and CARED –> CAR·RI·ED. Then, you could remove the AR out of CARRIED and you’re left with CRIED. Note that you couldn’t remove the IE slice out of CARRIED, because CARRD is not a word, nor could you remove the RI because the new two-letter slice must be different.


The puzzle

Start with: AL

  1. SEED
  2. BRING
  3. POLE
  4. BANS
  5. TIGHT

Solution:
| insert | into | word | pull | leaves | |---|---|---|---|---| | AL | SEED | SE·**AL**·ED | EA | SLED | | EA | BRING | B·**EA**·RING | AR | BEING | | AR | POLE | P·**AR**·OLE | RO | PALE | | RO | BANS | BA·**RO**·NS | ON | BARS | | ON | TIGHT | T·**ON**·IGHT | TO | NIGHT |