How big a crossword puzzle can you make without using any blank squares? Only the solution is required, not the clues.
Here is a 6x6 example, the solution to a recent puzzle by @Avon.
A B A S E S B A N A N A A N G L E D S A L A M I E N E M A S S A D I S T
Answers are sought in five categories:
- 1) puzzles with a square grid, where all rows and columns are of equal length
- 2) puzzles with an oblong grid, where all rows are of equal length and so are all columns but rows are longer than columns
- 3) puzzles with a jagged right-hand edge, where all down words start in the first row
- 4) puzzles with a jagged right-hand edge, where one or more down words do not start in the first row, and where columns that contain two or more (disjoint) words are allowed
- 5) the same as 4), but with the added requirement that every letter must be in both an across word and a down word
In each category
- all words contain two or more letters
- all words contain contiguous letters only
- each horizontal or vertical string of contiguous letters that isn't contained within another such string forms a word, and we're not interested in words that are contained in other words
- there are no blanks: in other words, no empty space is adjoined in all four cardinal directions by letters
- all letters not in the top row are under a letter in the top row, and all letters not in the leftmost column are to the right of a letter in the leftmost column
The third condition rules out the type of crossword that instead of using blanks uses small blocker lines between squares, like this:
The last condition rules out puzzles such as
P R E S T I D I G I T A T I O N A T P A T A T A T . .
in all categories, each row only contains one word, beginning at the left edge of the grid.
in the first, second and fifth categories, each letter is in both an across word and a down word
An example of a puzzle in the second category:
A P E S L I K E L E E T
One in the third:
F E T C H A R E N E A T
Two in the fourth:
M A T C H A R L I E N T A R O
S K I T C A N O R O M E N T A R O
One in the fifth:
E T A M A T O R T E A E S H
In each category, there will be
- a) a winner with the most letters
- b) a winner with the most words.
(In the first category, these will be the same puzzle.)
In the second category, there will be three additional classes of winner:
- c) a winner for each number of rows, being the oblong with the most columns
- d) an overall row winner, with the largest number of rows
- e) an overall column winner, with the largest number of columns
Letters and words are counted with multiplicity.
Other interesting classes of winner may well be suggested as time goes on!