# Farmer needs to get his word across the river

In the spirit of the classic river-crossing puzzles:

Problem:

The word PLANS is on the west shore of a river, while the word PAINTER is on the east shore.
The farmer needs to take his word PLANS from the west side to the east side.
However, he can only cross the river with one "chunk" at a time,
and the words on both shores must be valid words at every intermediate step.

----------------------------------------------------------------------------------------

Solution:

PLANS            PAINTER
|            .   |
|          .     |
|        ER      |
|      .         |
v    .           v
PLANERS           PAINT
|    .           |
|      .         |
|       ERS      |
|          .     |
v            .   v
PLAN             PAINTERS
|            .   |
|          .     |
|       TER      |
|      .         |
v    .           v
PLANTER           PAINS
|    .           |
|      .         |
|       LANT     |
|          .     |
v            .   v
PER             PLANTAINS
|            .   |
|          .     |
|       TAIN     |
|      .         |
v    .           v
PERTAIN           PLANS


A "chunk" is a string of consecutive letters taken from anywhere within the word. It can also be inserted anywhere into the other word. It must consist of at least two letters (no single-letter chunks), but there is no length limit. The chunk does not need to be a valid word.

Notice that the farmer succeeded in moving his word PLANS from the west shore to the east shore, but the other word did not survive in its original form. There is no requirement to keep the other word in its original form.

Although the above example happens to show the movement of the chunks alternating between east-to-west and west-to-east, this is not a requirement. The farmer is permitted to ferry an empty boat from one shore to the other whenever he deems necessary.

Now you try it:

Problem:

The word RETESTED is on the west shore of a river, while the word INGRAIN is on the east shore.
The farmer needs to take his word RETESTED from the west side to the east side.
However, he can only cross the river with one "chunk" at a time,
and the words on both shores must be valid words at every intermediate step.

• What counts as a valid word, exactly?
– Deusovi
Commented Jul 16, 2019 at 23:20
• @Deusovi — Always a good question. Any distinguishable English word in any part of speech, inflection, or variant. For example, these are all distinguishable words: RUN, RUNS, RAN, RUNNING, FAST, FASTER, FASTEST, QUICK, QUICKLY, GREEN, COW, COWS, CATTLE. As I'm always wary of ambiguity and controversy, I craft my puzzles using well-known words only, without capitalization, hyphens, apostrophes, slang, acronyms, etc. (Intuitive definition of "well-known": Could I imagine seeing this word used in a local American newspaper?) Commented Jul 17, 2019 at 0:17

You can do it like this:

RETEST(ED) INGRAIN
RETEST (ING)RAINED
R(ET)ESTING RAINED
RESTING RE(TA)INED
RESTATING RE(IN)ED
REIN(STAT)ING REED
REINING RES(TA)TED
R(ET)AINING RESTED
RAINING RETESTED

On each line other than the last, parentheses indicate what is to be moved to the other side.