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Below is a 7x7 square grid. On the top row is a single word with seven letters. From the permutation of the letters of this word, one word has been created. Is it possible to create a solution with 15 words (Merriam-Webster online dictionary) from a single 7-letter word (of your choice) in the top row, using permutations? Words can be read horizontally, vertically and diagonally. The following restrictions apply: No two same letters are allowed to appear in any row any column or in either of the two diagonals.

letter grid containing permutations of the word 'century' and the word CENT next to it. Replicated below.

addendum: If you put the word ARTICLE in the top row and then perform the permutations in the sequence of the given example, then more than 10 words are created. Here are 10 of them: ART, ARTIC, EAR, LEA, CLEAR, RECTAL, TIC, LEAR, IRE, TALI.

2nd addendum: The word maximum was not intended to be interpreted with mathematical meaning, because it is impossible to calculate the maximum number of word with traditional mathematical methods. I changed the wording of the puzzle.

As a table for accessibility:

1 2 3 4 5 6 7
C E N T U R Y
R Y C E N T U
T U R Y C E N
E N T U R Y C
Y C E N T U R
U R Y C E N T
N T U R Y C E

CENT

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    $\begingroup$ I’m voting to close this question because without defining "word" it turns into an ill-defined, open-ended puzzle (and open-ended puzzles are off-topic as of May 2019) $\endgroup$
    – bobble
    Dec 12, 2021 at 2:07
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    $\begingroup$ Okay, now you've edited in a dictionary (note to the two people who pinged me about my wrongness: the edit happened after my comment). Are computer solutions allowed? That's the only real way I can see to prove optimality $\endgroup$
    – bobble
    Dec 12, 2021 at 15:18
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    $\begingroup$ So is the question really "find a solution with 10 words"? $\endgroup$
    – bobble
    Dec 12, 2021 at 19:59
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    $\begingroup$ This "puzzle" is really a game whose objective is to find the best solution one can. As @bobble pointed out, this community decided that such open-ended questions are off-topic here. Two suggestions, if you want to salvage this: (1) set a specific provable goal like you did in the comments—make the question "Does a solution with 10 words exist?"—since at that point the question is one that can potentially be provably answered; (2) OED is a great decider of what-is-a-word in principle, but in practice many people cannot access it... consider a different, publicly accessible dictionary. $\endgroup$
    – Rubio ♦
    Dec 16, 2021 at 21:31
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    $\begingroup$ But doesn't that turn this back into a game? $\endgroup$
    – bobble
    Dec 17, 2021 at 4:40

1 Answer 1

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Am I missing something? Thanks to @PuzzleFerret to pointing out a rule I missed originally, but the answer still seems trivial. What did I miss this time?

Full solution:

  1. put the word ARTICLE in the top row and then perform the permutations by shifting each row twice:

ARTICLE
LEARTIC
ICLEART
RTICLEA
EARTICL
CLEARTI
TICLEAR

  1. find 15 words horizontally, vertically and diagonally, that are in the MW dictionary

Well, okay. 10 are given to us:
1)ART
2)ARTIC
3)EAR
4)LEA
5)CLEAR
6)RECTAL
7)TIC
8)LEAR
9)IRE
10)TALI

And here are the next 5:

11)TI
12)IT
13)AE
14)AT
15)EL
I now have no idea if reading backwards is permitted; the question seems ambiguous in that respect. But if so, just substitute RE or other words.

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