`The object of this game is to place as many numbered squares on
the board as possible. There are of course several limitations:
`

- The numbering of a square cannot exceed the size of the board. Thus
on a 9x9 board, only the numbers from 1-9 are allowed.
- If two squares have the same number, they cannot share the same row
or column.
- If two squares A and B have the same number, then no other numbered square can simultaneously share a row with A and a column with B.

The score is measured as ` log(N)/log(n)`, where N is the number of
numbered squares, and n is the size of the board. The highest score ever
achieved is `log(6)/log(3)=1.63..`, which one can attain whenever
n is a power of 3.
On the other hand, it's known that one cannot exceed `25/13 = 1.923...`.

To place or remove a square, simply click on the board. To change the numbering of the square, press the appropriate numeric key (1-9) or use the choice bar on the right-hand side. Blacked out squares cannot be occupied by any new square; red-colored squares cannot be occupied by squares with the currently selected number.

Press the space bar to clear the board.

On the right I've displayed the number of squares
you need to beat the world record of `log(6)/log(3)`; if you
ever do beat this, please save the configuration to the Java console
using the 'S' key, and send me an e-mail!

This game arose from the study of sums and differences of numbers in a finite set, and has application to the Kakeya problem in combinatorial geometry.