An equilateral triangle with the side length 7 is divided into 49 small equilateral triangles with the side length 1, as it is shown on fig. 28. Parallelograms with side lengths 1 and 2 are cut from the triangle along the grid lines. What is the greatest number of parallelograms that can be cut in this way?
Fig. 28
Solution
Paint the small triangles in black and white as it is shown on fig. 29. Since every parallelogram with the side lengths 1 and 2 contains two white triangles, and the total number of white triangles is 21, the number of parallelograms does not exceed 10.
On the fig. 30 it is shown how one can cut 10 parallelograms.
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