A colony of termites has attacked a house by carving out passageways trough the floorboards. The damage done is proportional to the number of triangles and right now there are 27 of them: 16 small, 7 medium, 3 large, and 1 huge.

Which of the 15 intersections would you fill to minimize the number of triangles?
Is your solution unique?

If you wanted to get rid of all triangles; how many intersections would you have to fill?

Extensions:

Parker & Jordan from Bishop Pinkham asked people to destroy all the squares by filling in the fewest number of intersections. On the right is an answer using 7 intersections. Notice that each square goes through one of the red intersections. Solve their problem using only 6 intersections.

It took the termites 30 passageways to create 27 triangles. Prove that the number of triangles are always less than the number of passageways, or give a counter-example.

Create your own problem on your own grid. For more grid patterns see one of these web sites: mathworld or wikipedia.

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