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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:

crossword with blockers

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
          . . 

Note that

  • 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!

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  • $\begingroup$ There is another type of crossword without blanks like this one but they aren't as much of a challenge to make. $\endgroup$ – Bob May 23 '15 at 17:49
  • $\begingroup$ Yes - the Sunday Times magazine used to have ones like that, and maybe still does. They're ruled out by the third point under the words "in each category", but is there a description or name short enough to rule them out in the title? If so, it should go in. I can't think of anything shorter than "crosswords with some words ending at lines between squares, not at blanks". $\endgroup$ – h34 May 23 '15 at 17:57
  • $\begingroup$ @Bob - Thanks for your comment. I've now changed the title to say "without blanks or blockers" and added some words to the question to make clearer that that type of crossword isn't what's meant. $\endgroup$ – h34 May 23 '15 at 19:01
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1) WORD SQUARE: The maximum length is 9 letters, or 10 if you extend the dictionary with personal names, geographic nouns, and so on...
Example of 9:

A C H A L A S I A
C R E N I D E N S
H E X A N D R I C
A N A B O L I T E
L I N O L E N I N
A D D L E H E A D
S E R I N E T T E
I N I T I A T O R
A S C E N D E R S

Example of 10:

D E S C E N D A N T
E C H E N E I D A E
S H O R T C O A T S
C E R B E R U L U S
E N T E R O M E R E
N E C R O L A T E R
D I O U M A B A N A
A D A L E T A B A T
N A T U R E N A M E
T E S S E R A T E D

2) WORD RECTANGLE: The biggest known word rectangles seem to be 8x4 and 7x6. This is 8x4:

D E C I M A T E
A V O C A D O S
N A M E L E S S
E S P R E S S O

and this is 7x6:

A M E R I C A
M A R A C A S
B U R G E S S
I M I T A T E
T A N A G E R
S U G G E S T

3) "LEFT" CROSSWORD: The biggest I've found is a 13-length half square:

T O S H A M A B R A H A M
O B T E N E B R A T E S
S T R A I T L A C E D
H E A D S H A K E S
A N I S O A T E S
M E T H A N O L
A B L A T O R
B R A K E L
R A C E S
A T E S
H E D
A S
M

4) RIGHT-JAGGED CROSSWORD: I suggest a 10-length half square.

P
R A
O R S
G R E W
R E X E S
E S T A T E
S T O N I N G
S I L E N T L Y
E V E R G R E E N
S E T S E Y E S O N

5) RIGHT-JAGGED ADVANCED CROSSWORD: Again, I propose the same crossword of the fourth contest.

Credits: most of my material comes from the National Puzzlers' League

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  • $\begingroup$ Wow! Imagine having that 10-square on a talisman! :-) But although the set of solutions for q4 includes the one for q5, it's disjoint from the one for q3. What can you do with say 2 or 3 rows for q2? Scrabblers should be good at that - practically all keen players know their canonical list of 2-letter words, whether SOWPODS or some other variant. $\endgroup$ – h34 May 23 '15 at 22:14
  • $\begingroup$ @h34 I've edited number 4 and indirectly 5 $\endgroup$ – leoll2 May 24 '15 at 8:29
  • $\begingroup$ Are you sure about the 9/10 letter maximum for the word square? I have no idea if bigger is possible, but the examples you give are constrained to have the same words down and across. I wonder if one could get larger if that constraint were relaxed (which is allowable for this question). $\endgroup$ – user2390246 Mar 24 '16 at 17:41
  • $\begingroup$ Oh, and surely SETSEYESON in number 4 is not valid? Still a great answer though! $\endgroup$ – user2390246 Mar 24 '16 at 17:44
  • $\begingroup$ @user2390246 - Many crosswords allow for multiple word entries. $\endgroup$ – Darrel Hoffman Apr 5 '16 at 19:03

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