I was the winner of NPR's Sunday Puzzle a few weeks ago that he refers to on his website. I used a program to find the best grid. As he states, there was only one 3x3 grid that has ALL 2-letter elements in it (which Will Shortz seemed to know even though I didn't tell him).
Anyway, he is right that it takes a very long time to generate all the grids when you go above 3x3. An easier problem is generating all possible Word Squares. I did this a few weeks ago after being motivated by the previous Slashdot post about a 10-letter word square. It's much easier to narrow down the Depth First Search in this situation (every row is the same as every column). I used C++.
Interestingly enough, not only are there no 10-letter word squares, there are no 9-letter ones either. And, there are only five 8-letter word squares.
A distribution of the results as well as the 8-letter squares can be found here.
Slashdot Mirror
Hi,
I was the winner of NPR's Sunday Puzzle a few weeks ago that he refers to on his website. I used a program to find the best grid. As he states, there was only one 3x3 grid that has ALL 2-letter elements in it (which Will Shortz seemed to know even though I didn't tell him).
Anyway, he is right that it takes a very long time to generate all the grids when you go above 3x3. An easier problem is generating all possible Word Squares. I did this a few weeks ago after being motivated by the previous Slashdot post about a 10-letter word square. It's much easier to narrow down the Depth First Search in this situation (every row is the same as every column). I used C++.
Interestingly enough, not only are there no 10-letter word squares, there are no 9-letter ones either. And, there are only five 8-letter word squares.
A distribution of the results as well as the 8-letter squares can be found here.
Jeff Terrace