# The smallest crossword

I heard Martin Gardner in one of his books presented a crossword, which looks like 3x3 square. Could you help me to find it?

Also, have been there a smaller crossword puzzle created?

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Normal crossword rules prohibit words less than three letters. Accepting that (and ignoring the empty puzzle), the smallest is $3 \times 3$ –  Ross Millikan Jun 17 '14 at 14:13

I found the book: M.Gardner "Aha. Insight.", p. 153.

Here is the crossword, which was called there "World's smallest crossword":

The clues are:
Horizontal: 1. Insect 4. To annoy 5. Eavesdropper
Vertical: 1. Stingers 2. To employ 3. Gigi has two
(There are typos in numbers 4 and 5).

Solution:

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The numbers on the horizontal clues should be $1,4,5$. I presume that was in the original source. –  Ross Millikan Jun 17 '14 at 20:25
what is the solution to this one? –  Kate Gregory Jun 18 '14 at 16:22
@KateGregory, i added it. –  klm123 Jun 18 '14 at 16:25
groan. What is written on the bottle in the hands of the creature on the right? –  Kate Gregory Jun 18 '14 at 16:27
@kaine imagine the transformation "Cat cat cat" --> "cats". Use that on each vertical entry, and then say it aloud. It will sound just like a word that is actually the answer to the vertical clues. –  Kate Gregory Jul 13 '14 at 17:35

It's not hard to construct a 1x1 crossword:

+---+
|1  |
|   |
+---+


Across:

1. A Roman one.

Down:

1. The shortest pronoun.

There's also a cheating one going around, with clues "What letter am I thinking of?" and "What is the answer to 1 Across?", and claimed solution "I'm thinking of U".

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Shouldn't crossWord have Words in it? –  klm123 Jun 17 '14 at 9:00
From wiki: A crossword is a word puzzle that normally takes the form of a square or a rectangular grid of white and black shaded squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the answers. –  klm123 Jun 17 '14 at 9:01
All English dictionaries list at least two one-letter words. (Spanish crosswords, or at least the ones I do, will use any single letter as a word where necessary, because they have a different structure). –  Peter Taylor Jun 17 '14 at 9:23
A crossword doesn't necessarily have the same restrictions on possible words as Scrabble does. Abbreviations, acronyms, and proper nouns are all fair game in a crossword puzzle. Therefore, any of the $26$ English letters can theoretically appear by itself in an English crossword. –  Joe Z. Jun 17 '14 at 13:52
(In practice, though, an American crossword is designed in a way so that no word is shorter than 3 letters.) –  Joe Z. Jun 17 '14 at 13:53

What a about the null crossword, presented below. It has no clues. This is the smallest crossword possible and yet impossible to solve. (Or not solve.)

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George Perec actually jokingly designed a 1x1 grid, with the following clues:

Horizontalement : 1. Voyelle

Verticalement : 1. Consonne

see French Wikipedia.

In Italian, you may find a lot of examples in the site of Aldo Spinelli.

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As Peter Taylor mentioned, it's possible to make a $1 \times 1$ crossword. Since crosswords don't necessarily have to use whole words in the English language like Scrabble does (abbreviations and proper nouns are totally fair game in crosswords), it's possible to use any of the $26$ letters in the single square, for a total of $26$ possible combinations.

If you get up to $2 \times 2$, there are four essentially distinct ways to block off squares that don't convert it into just a $1 \times 1$:

+---+---+    +---+---+    +---+---+    +---+---+
|1  |2  |    |1  |   |    |1  |xxx|    |1  |xxx|
|   |   |    |   |   |    |   |xxx|    |   |xxx|
+---+---+    +---+---+    +---+---+    +---+---+
|3  |   |    |   |xxx|    |   |xxx|    |xxx|2  |
|   |   |    |   |xxx|    |   |xxx|    |xxx|   |
+---+---+    +---+---+    +---+---+    +---+---+


The last one, however, is just two $1 \times 1$s superimposed on a $2 \times 2$ board, which is uninteresting.

Each of these has multiple options for what words can go into them, which are hard to enumerate here.

If you are going by the rule that a crossword word must have at least three letters, the smallest grid you can make is $3 \times 3$, simply because a smaller grid can't fit a three-letter word into it. There are two ways such a grid can be made:

+---+---+---+    +---+---+---+
|1  |2  |3  |    |1  |   |2  |
|   |   |   |    |   |   |   |
+---+---+---+    +---+---+---+
|4  |   |   |    |   |xxx|   |
|   |   |   |    |   |xxx|   |
+---+---+---+    +---+---+---+
|5  |   |   |    |3  |   |   |
|   |   |   |    |   |   |   |
+---+---+---+    +---+---+---+


and again, a multitude of ways the letters can be filled in to make words.

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Your second $3 \times 3$ has unchecked letters, which are not (normally) allowed in US crosswords and required in British crosswords. I would say there is only one diagram for each side of the pond. –  Ross Millikan Jun 17 '14 at 15:26
Oops, forgot about that. –  Joe Z. Jun 17 '14 at 16:26
Also, classical crossword symmetry rules eliminate all but the 'no blocks' and 'superimposed 1x1' fills of the 2x2 grid, and substantially limit even the 4x4 case; factoring in the 'at least 3 letters' restriction and the symmetry restriction yields only two valid 4x4 grids, the no-blocks grid and a grid with blocks at top left and bottom right. –  Steven Stadnicki Jun 17 '14 at 19:34

The following is inspired by an old Swedish crossword puzzle, whose solution has the same structure.

Across: 1. Apex

Down: 2. Burden

+---+---+
|xxx|2  |
|xxx|   |
+---+---+
|1  |   |
|   |   |
+---+---+


Solution:

X W
H 8

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