Cleave Books
Pentominoes
Space-filling Problems 3

12 pentominoes (each made of 5 squares) must cover between them, a total of 12 x 5 = 60 squares.
One of the ways this can be done is by filling a rectangle measuring 3 by 20.
Such a rectangle, with just 3 pentominoes placed in it is shown below. It is the start of a solution.

 16 Find the complete solution to filling the 3 by 20 rectangle.

 A rectangle of area 40 squares can be filled with 8 pentominoes. One way of doing this is in a 5 by 8 rectangle and one is shown on the right. 17. Find a way of covering the same area but in a 4 by 10 rectangle.
 18. Cover an area of 45 squares in a 5 by 9 rectangle. 19. Fill a rectangle of area 50 squares. 20. Fill a rectangle of area 55 squares. Using all 12 pentominoes to fill a rectangle can be done in 3 different ways. As a 3 by 20 rectangle; as a 5 by 12 rectangle; as a 6 by 10 rectangle. The 3 by 20 was done in problem #16 (above). One solution to the 5 by 12 (from among several thousand) is shown below. 21. Find a different way to fill the 5 by 12 rectangle. 22. Use the full set of 12 pentominoes to fill a 6 by 10 rectangle.