The Prague Czecherboard Puzzle

For the 28th International Puzzle Party, held in Prague (the Czech Republic) in August 2008, Kate designed a puzzle with a pun in its theme. The Prague Czecherboard puzzle consists of 36 square pieces, with the letters P R A G U E cut out of them 6 times. Each letter is unevenly divided between red and blue, though there are 18 of each color, representing the Czech flag.

They are to be solved with three conditions simultaneously, mingling the themes of Latin squares, checkerboards, and Sudoku (see below). We have a few of this limited edition design still available, while they last.     \$22

Our challenge to the world was to solve this puzzle with more than 18 rectangles of 2x3 that contain all 6 letters, while also following goals 1 and 2. The first solver would win a prize.

Update—December 6, 2008:
Solved! Jay Berkenbilt sent us his computer-assisted solution containing 23 separate and overlapping 2x3 rectangles containing all 6 letters. He also found intermittent solutions with 19, 20, 21 and 22 rectangles. Jay believes that 23 is the maximum possible. He wins the prize, and this contest is now closed. (Unless your computer can beat that 23...)

 Who We Are