Problem of the Week 1063

Make Triangles

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Using 4 line segments one can make a figure yielding two (interior disjoint) triangles, as shown at left below. Using 6 line segments, it is possible to make a figure yielding seven (interior disjoint) triangles, as shown at right.

How many (interior disjoint) triangles can you get using 7 line segments?

Source: This is known as the "Kobon triangle" problem. I saw it in Ed Pegg's Feb 8, 2006, Math Games column at the MAA site.

© Copyright 2006 Stan Wagon. Reproduced with permission.