**Quadrata** puzzles are based on Latin Squares that were developed by the 18th century
mathematician Leonhard Euler, who used letters of the Latin alphabet, hence the name.
On the left and right, you can see stained glass windows that use Latin squares only instead
of letters, the cells have various colours of stained glass. As you can see from the glass, no
colour is repeated in the same column or row.

*Just in case you are curious as to why the borders of the sheets of colourless glass
around the edge don't match up with the borders of the coloured cells, the reason is that
a line of flexibility - where you have a straight line of
lead came which is soft and easily bent and in effect can become a hinge
- is broken by the solid glass at this point therefore the window has a lot more strength and
will keep its shape better.*

With the original Latin squares, there were letters but, you can see that it doesn't matter
whether it is letter, numbers or coloured glass, the principle is the same.

One property of numbers is that they have a natural order so if you use an inequality sign
(> and <) between two cells you can constrain which values can go in those cells -
if there is a 3 in a cell and the cell on the other side of the inequality is defined as less
than that, you know that it can only be a 1 or 2. If a 2 is used up in a different cell in
that cells column or row, you know it can only be occupied by a 1.

You can see from some of the puzzles on this site and in the books that you don't necessarily
need to have any explicit values given to you for the puzzle for it to become soluble although
this becomes less the case the larger the puzzle gets.

However, unlike the 'more or less' and Futoshiki puzzles you will find, Quadrata puzzles
are not limited to numbers because, if you define the order of the values,
you can have anything in there - theoretically, you can have
**mouse < cat < sheep < horse < elephant** and it will still work although you would probably
have to make the cells larger and rely upon the abilities of the reader which might shift the
emphasis away from puzzle solving and towards artistic skills.

So limiting our cells to providing homes for numbers and letters of the alphabet, we have
numbers and letters:

- Numbers are relatively easy because you don't have to think about the order.
- Letters in the form of words are not ordered quite as obviously as numbers but if you look
at the words, you can work it out without too much trouble. The only trouble really is finding
enough words that don't have any repeating letters in them that are long enough. Once you get to
around an 9x9 puzzle, the words are getting scarce enough for two words to be used so then the
problem is finding a pair of words that between them, don't have any repeating letters and in
English, there are only five vowels. As a result, at 19x19, you end up with things such as:
**G**<**U**<**N**<**P**<**O**<**W**<**D**<**E**<**R** < **B**<**L**<**A**<**C**<**K**<**S**<**M**<**I**<**T**<**H**
**B**<**L**<**A**<**M**<**E**<**W**<**O**<**R**<**T**<**H**<**Y** < **D**<**U**<**C**<**K**<**P**<**I**<**N**<**S**
**O**<**V**<**E**<**R**<**F**<**L**<**Y**<**I**<**N**<**G** < **H**<**U**<**M**<**P**<**B**<**A**<**C**<**K**<**S**
**U**<**N**<**C**<**O**<**M**<**B**<**E**<**D** < **P**<**L**<**A**<**Y**<**W**<**R**<**I**<**G**<**H**<**T**<**S**

which play with the imagination.
- Letters would be a lot easier if they were just ABCDEF... and so on so, with a view to
making it more interesting, the letters are randomised.

Just like the Sudoku, Kakuro and Gogen puzzles, every day,
I put brand new, unique, Quadrata puzzles on this web
site for you to print out and solve and it doesn't cost you a thing.
Also, like the Kakuro and Gogen puzzles, they get harder as the week goes on.

Again, these puzzles are produced by my computer, only for this site,
using a computer program that I wrote myself in Perl. The solver part of my
program uses logic only, it does not use brute-force and as a result of this,
you will be able to solve them using just logic and yes, those with no
letter clues in them are possible to do as well.