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Our daughter recently conned my wife and I into purchasing interlocking foam squares for her bedroom floor. On each square is a different letter of the alphabet. To cover her entire floor we had to purchase 4 packages. After moving all her furniture to one side of the room I commenced laying out the squares. When I got to the 'K' square in the first package our daughter asked, "How many words can it make?"

With a grid measuring 8 x 13 my question would seem somewhat elementary:

Given 4 packages of interlocking foam squares, with each package containing 26 interlocking pieces, each bearing a different letter of the alphabet A-Z, and using standard word search rules, what is the optimal arrangement of letters such that it yields the maximum number of distinct words?

For reasons too ridiculous to mention one of the perimeter rows measuring 13 must contain two of the "B"'s side by side... See diagram

I thought there might be a computer I could pose the problem to?

8 by 13 grid with two Bs side by side on top row

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  • $\begingroup$ Are you asking for the optimal arrangement of letters such that it yields maximum number of distinct words? $\endgroup$
    – justhalf
    Commented Jan 24, 2017 at 15:30
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    $\begingroup$ Even with a computer I don't think it's feasible to answer this problem. It's a lot more complex than you would think 8*13 = 104. there are 104 * 103 * 102 * 101 ... and so on possible ways to lay down the tiles. This number is HUGE!! it doesn't account for the duplicate letters but I think those get removed by dividing by 26 * 4! but that still is huge $\endgroup$
    – Ivo
    Commented Jan 24, 2017 at 15:39
  • $\begingroup$ With only 4 of each vowel, though, you'd be lucky to use them all. $\endgroup$
    – Gordon K
    Commented Jan 24, 2017 at 16:41
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    $\begingroup$ I’m voting to close this question because open-ended puzzles are off-topic as of May 2019 $\endgroup$
    – bobble
    Commented Jul 20, 2021 at 17:55
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    $\begingroup$ Then - 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
    Commented Oct 18, 2021 at 18:05

1 Answer 1

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Although comments claim this is impossible to compute, I think once you take into consideration that every word needs at least 1 vowel, and you're extremely limited in that respect, it knocks down the possibilities tremendously.

As for me, I wont try to establish every possibility, but I've come up with a list of words that exclude only fgjjjkqqwxxz.

Words include some cross-overs, all read left to right, or up to down: scrabble, rhythm, strength, craftsmanship, known, quizzed, foxy, quick, guppy, comb, blimp, daddy, fuzz, act, flex, strong, plow, thick, dew, and jug.

Add the remaining letters where you like.

enter image description here

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    $\begingroup$ Good attempt. Maybe this question is a good fit for codegolf.stackexchange.com, as a competition to get the highest number of words in the grid. $\endgroup$
    – justhalf
    Commented Feb 1, 2017 at 4:39

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