Puzzle: Perfect rectangles, perfectly tiled with distinct squares, squaring the rectangle

. . .

Solutions to Perfect rectangles nrs 11 to 20

All solutions are found with backtracking. They are ordered by the length of the long side. Only original (simple) solutions have got a number.

====================== 88x65 ======================

11. 88 x 65 rectangle, with 18 squares
Without using the 1x1 square.

====================== 88x74 ======================

12. 88 x 74 rectangle, with a new record of 22 squares!
If you found it with your bare hans, you deserve a friendly bat on your back :-)

====================== 89x71 ======================

13. 89 x 71 rectangle, with 20 squares

====================== 89x80 ======================

14. 89 x 80 rectangle, again with 22 squares
The 1x1 piece is not used in this solution

====================== 91x81 ======================

15. 91 x 81 rectangle, with 18 squares

====================== 94x63 ======================

16. 94 x 63 rectangle, with 17 squares

====================== 97x65 ======================

97x65 is not printed, it is a 'short' fibonacci development of the 33x32 rectangle

====================== 97x94 ======================

17. 97 x 94 rectangle, with 18 squares
The 1x1 piece is not used in this solution

====================== 98x65 ======================

98x65 is not printed, it is a 'long' fibonacci development of the 33x32 rectangle
At length 98 there also exist several original solutions, they all need a low number of squares...

====================== 98x97 ======================

18. 98 x 97 rectangle, out of 13 squares
Almost square solution, without using the 1x1 square.

====================== 98x95 ======================

19. 98 x 95 rectangle, with 11 squares
The 1x1 piece is not used in this solution

====================== 98x86 ======================

20. 98 x 86 rectangle, with 11 squares too

===================================================

Solutions 21 upto 30

back to perfect rectangles overview