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.

pentomino 3x20
16. Find the complete solution to filling the 3 by 20 rectangle. If you need it you can get a hint.
17. A rectangle of area 40 squares can be filled with pentominoes.
One way of doing this is in a 5 by 8 rectangle and one is shown on the right.
Find another way of doing it in a 4 by 10 rectangle.
pentomino 5x8
18. If you solved the triplication problem [#8] for the I-pentomino then that created a 3 by 15 rectangle having an area 45 squares.
Now find a way of filling a 5 by 9 rectangle which also has an area of 45 squares.
19. Find a way of filling a rectangle of area 50 squares.
20. Find a way of filling 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 #15 (above).
One solution to the 5 by 12 (from among several thousand) is shown below.
pentomino 5x12
21. Use the full set of 12 pentominoes to fill a 6 by 10 rectangle.

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