OFFSET
1,3
COMMENTS
The n X n crossword puzzle grid must contain the maximum number of 3-letter words (and no words of other lengths), and all words must be interconnected (i.e., no word or set of connected words can be completely separated from the other words).
The magazine Humor y Juegos Number 13 says that Mariano Pablo Amieva and Solomon Golomb found a general answer to this problem.
REFERENCES
Jaime Poniachik, Las matemáticas del crucigrama, Revista Humor y Juegos, Número 9, ~ 1981.
LINKS
Rodolfo Kurchan, Problem 781, Puzzle Fun 35, December 2021.
EXAMPLE
4 X 4 solution with a(4) = 6 words by Jaime Poniachik:
+---+---+---+---+
| | | |XXX|
+---+---+---+---+
|XXX| | | |
+---+---+---+---+
|XXX| | | |
+---+---+---+---+
|XXX|XXX|XXX| |
+---+---+---+---+
.
5 X 5 solution with a(5) = 8 words by Jaime Poniachik:
+---+---+---+---+---+
| | | |XXX|XXX|
+---+---+---+---+---+
| |XXX| | | |
+---+---+---+---+---+
| | | |XXX| |
+---+---+---+---+---+
|XXX| |XXX|XXX| |
+---+---+---+---+---+
|XXX| | | |XXX|
+---+---+---+---+---+
.
6 X 6 solution with a(6) = 12 words by Jaime Poniachik:
+---+---+---+---+---+---+
| | | |XXX|XXX| |
+---+---+---+---+---+---+
|XXX| |XXX| | | |
+---+---+---+---+---+---+
|XXX| | | |XXX| |
+---+---+---+---+---+---+
| |XXX| | | |XXX|
+---+---+---+---+---+---+
| | | |XXX| |XXX|
+---+---+---+---+---+---+
| |XXX|XXX| | | |
+---+---+---+---+---+---+
.
Example of an invalid solution: a 6 X 6 solution with a(6) = 12 words, but not valid because some words have 2 letters instead of 3, and the 3-letter words are not all interconnected (black squares completely separate the set of 3-letter words at the upper right from the set of 3-letter words at the lower left):
+---+---+---+---+---+---+
| | |XXX| | | |
+---+---+---+---+---+---+
| | |XXX| | | |
+---+---+---+---+---+---+
|XXX|XXX|XXX| | | |
+---+---+---+---+---+---+
| | | |XXX|XXX|XXX|
+---+---+---+---+---+---+
| | | |XXX| | |
+---+---+---+---+---+---+
| | | |XXX| | |
+---+---+---+---+---+---+
.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Rodolfo Kurchan, Feb 12 2022
STATUS
approved