# Smallest rectangle to put the 24 ABCD words combination

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

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

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

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

Second attempt, based on suggestion from @Rodolfo Kurchan:

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

• Hi, in the solutions can be only 4 letter words, in this solution there are some 3 letter words Commented Apr 6, 2023 at 23:20
• 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 Commented Apr 6, 2023 at 23:23
• 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 Commented Apr 7, 2023 at 1:26

Pretty sure that the following is minimal.

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

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":

• Hi, in the rectangles can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters Commented Apr 7, 2023 at 18:51
• @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. Commented Apr 7, 2023 at 18:58
abcd  cabd  cbda  bacd  dbac