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26 Words

Solution written by Tahnan

(1) Use the 5's as a breakin. That provides REACT, TRACE, CRATE, EARTH, HEART, SQUID, QUIDS. That's a pretty good starting point. Then work out the P--with three overlaps with SQUID, the only word it can be is PIQUE. (Well, OK, I missed PIOUS. All for the best, though.)

(2) Pick a letter with either a lot of 0's, or a lot of overlap with words I have, or both. For instance:


(Bars indicate known words.)

(3) Eliminate the letters with 0's; mark all other letters as possible, but unmark letters in any known word with a 0 overlap:


(Bars in the top row indicate letters that may be in the word; bars in the bottom indicate known words.)

(4) For known words with a non-zero overlap, note which letters are still possible for that word. Repeat as necessary. In this case: PIQUE has one letter of overlap, but I, Q, U, and E aren't possible; the overlap must be P. Similarly, HEART has one overlap, which must be the H. (As does EARTH; having used that information in H, we can go ahead and eliminate that.)

(5) With sufficient evidence, work out the word. In this case: the only word starting with G and containing a P, an H, and two of the letters KLMNOWXYZ is GLYPH.

(6) Return to step 2. I think I worked out X next, figuring that not many words started with X and that I stood a good chance of knowing it; then Y, with its heavy overlap with both REACT and EARTH. Then L; then, roughly, U, B, I, F, J...the more known words, the easier it gets, of course.

 

The complete list of words:
ACORN
BRAWN
CRATE
DRIVE
EARTH
FIRST
GLYPH
HEART
IRONS
JOKED
KLUTZ
LUMPY
MACHE
NACHO
OLIVE
PIQUE
QUIDS
REACT
SQUID
TRACE
UMBRA
VIXEN
WHITE
XYLEM
YACHT
ZILCH

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