8
$\begingroup$

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

enter image description here

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

enter image description here

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

$\endgroup$
0

4 Answers 4

10
$\begingroup$

\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}

$\endgroup$
3
  • 1
    $\begingroup$ Hi, in the solutions can be only 4 letter words, in this solution there are some 3 letter words $\endgroup$ 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 $\endgroup$ 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 $\endgroup$ Commented Apr 7, 2023 at 1:26
16
$\begingroup$

Pretty sure that the following is minimal.

All Permutations

$\endgroup$
3
  • 5
    $\begingroup$ Wow welcome to Puzzling Stack Exchange, glad to have you here! $\endgroup$
    – user78949
    Commented Apr 7, 2023 at 2:14
  • 1
    $\begingroup$ Welcome Ed, nice to see you. $\endgroup$ Commented Apr 7, 2023 at 12:21
  • $\begingroup$ It may not be minimal, but it certainly is elegant! The rotational symmetry is fairly neat! $\endgroup$ Commented Apr 12, 2023 at 10:38
1
$\begingroup$

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

$\endgroup$
2
  • $\begingroup$ Hi, in the rectangles can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters $\endgroup$ 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. $\endgroup$ Commented Apr 7, 2023 at 18:58
-1
$\begingroup$
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.

$\endgroup$
3
  • 1
    $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.