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Put in the smallest possible size board all combination of 4 quantity of letters. Crossword must be connected. And can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters

Example for:

ABC = 3 letters = 6 combinations in a 3x3 square

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Here is a solution for ABCD = 4 letters = 24 combinations in a 12 x 12 square = 144

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I am sure it is possible a solution in a smallest area rectangle

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4 Answers 4

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\begin{matrix} &1 &2 &3 &4 \\ 1 &A &D &B &C \\ 2 &C &B &D &A \\ 3 &B &A &C & \\ 4 &D &C &A &B \\ 5 & & & &A \\ 6 &A &B &D &C \\ 7 &C &A &B &D \\ 8 &D &D &C & \\ 9 &B &C &A &D \\ 10 & & & &C \\ 11 &C &D &A &B \\ 12 &A &A &B &A \\ 13 &D &B &C & \\ 14 &B &C &D &A \\ 15 & & & &D \\ 16 &B &D &C &C \\ 17 &D &A &D &B \\ 18 &A &C &B & \\ 19 &C &B &A &D \\\end{matrix}

Second attempt, based on suggestion from @Rodolfo Kurchan:

\begin{matrix} &1 &2 &3 &4 \\1&&B&&C\\2&&D&&B\\3&&C&&A\\4&B&A&C&D\\5&A&&D&\\6&D&A&B&C\\7&C&D&A&B\\8&&B&&D\\9&D&C&B&A\\10&A&&C&\\11&C&A&D&B\\12&B&C&A&D\\13&&D&&A\\14&D&B&A&C\\15&B&&C&\\16&C&A&B&D\\17&A&B&D&C\\18&&C&&A\\19&A&D&C&B\\\end{matrix}

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    $\begingroup$ Hi, in the solutions can be only 4 letter words, in this solution there are some 3 letter words $\endgroup$
    – Rodolfo Kurchan
    Commented Apr 6, 2023 at 23:20
  • $\begingroup$ You can try a similar solution in this board 1)XXXOOOOXOOOOXOOOOXO 2)OOOOXOOOOXOOOOXOOOO 3)XXXOOOOXOOOOXOOOOXO 4)OOOOXOOOOXOOOOXOOOO Sorry I don´t know how to show in 4 different lines $\endgroup$
    – Rodolfo Kurchan
    Commented Apr 6, 2023 at 23:23
  • $\begingroup$ Excellent solution. But now Bryce Herdt suggest to find a solution in this 5x15 rectangle of area 75 instead of the 4x19 rectangle of area 76 1) OOOOXXXXOOOOXOX 2) XOOOOXOOOOXOOOO 3) XOOOOXOOOOXOOOO 4) XOOOOXOOOOXOOOO 5) XXXXOOOOXXXXOXO $\endgroup$
    – Rodolfo Kurchan
    Commented Apr 7, 2023 at 1:26
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Pretty sure that the following is minimal.

All Permutations

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    $\begingroup$ Wow welcome to Puzzling Stack Exchange, glad to have you here! $\endgroup$
    – user78949
    Commented Apr 7, 2023 at 2:14
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    $\begingroup$ Welcome Ed, nice to see you. $\endgroup$
    – Dmitry Kamenetsky
    Commented Apr 7, 2023 at 12:21
  • $\begingroup$ It may not be minimal, but it certainly is elegant! The rotational symmetry is fairly neat! $\endgroup$
    – Matthieu M.
    Commented Apr 12, 2023 at 10:38
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I believe this 7x5 minimal answer satisfies the requirements of the problem as stated (all combinations of 4 letters and connected), employing the fact that, for example, the string "abcda" contains both "abcd" and "bcda":

Minimal solution to containing all four-letter combinations of a, b, c, and d

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  • $\begingroup$ Hi, in the rectangles can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters $\endgroup$
    – Rodolfo Kurchan
    Commented Apr 7, 2023 at 18:51
  • $\begingroup$ @RodolfoKurchan OK, I'll leave this here as a solution to the problem as originally written, though. I do believe the solution by Ed Pegg might very well be optimal for your additional requirements. $\endgroup$
    – Ben Hocking
    Commented Apr 7, 2023 at 18:58
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abcd  cabd  cbda  bacd  dbac
   cbad  bcad  bdac  adbc  d
dcba  badc  acbd  dacb  acdb
   bdca  adcb  cbda  cadb  a

Oops! It has duplicates. 27 sets not 24.

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    $\begingroup$ A 4x19 solution has already been posted (see the top accepted answer) $\endgroup$
    – bobble
    Commented Aug 2, 2023 at 21:44
  • $\begingroup$ The 4x19 accepted answer has 3 letter words. On of the stipulations was no words length 2,3,5 or more. $\endgroup$
    – TroyG
    Commented Aug 3, 2023 at 14:33
  • $\begingroup$ Check its second spoiler block $\endgroup$
    – bobble
    Commented Aug 3, 2023 at 14:42

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