Triangle and grids

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Kazi_Zareer
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Triangle and grids

Unread post by Kazi_Zareer » Thu Aug 04, 2016 9:59 am

There is a grid of equilateral triangles with a distance 1 between any two neighboring grid points. An equilateral triangle with side length $n$ lies on the grid so that all of its vertices are grid points, and all of its sides match the grid. Now, let us decompose this equilateral triangle into $n^2$ smaller triangles (not necessarily equilateral triangles) so that the vertices of all these smaller triangles are all grid points, and all these small triangles have equal areas.
Prove that there are at least $n$ equilateral triangles among these smaller triangles.
We cannot solve our problems with the same thinking we used when we create them.

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