CENTRE for INNOVATION in
MATHEMATICS TEACHING

PENTOMINOES
The Enclosure Problem


The drawing below shows the full set of 12 pentominoes arranged to enclose a 'field'.
Notice the rule used to join them is that they must touch along the full edge of a square and not just at the corners.

pentomino enclosure
It can be seen that an area of 59 (grey) squares is enclosed within the field.
It can also be noticed that the pentominoes have not been used very efficiently.
7. The problem is, to find a pentomino field enclosing the greatest possible area (= number of squares).
You can grade your attempts by reference to this table
AREAGRADE
under 70 not trying!
71 - 80 E
81 - 90 D
91 - 100 C
101 - 110 B
111 - 120 A
over 120 Super!
There are two variations on this puzzle -
1. That the outside edge of the enclosure must be a rectangle (having straight edges).
2. That the inside edge of the enclosure must be a rectangle (having straight edges).
The grading table given above does NOT hold for these variations.

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