## Thursday, August 30, 2007

### The Triangle Rearrangement Puzzle

You must have come across this puzzle many a times that said you have a triangle that have different tiles arranged in it. Now when you rearrange those tiles in the same triangle there is a place in the triangle that is unfilled. Now how can that happen?? Try it make cut outs on paper , rearrange them. It really happens, the first triangle was completely filled but later there is a tile of 1x1 size missing in the triangle
The puzzle rearrangement of triangle is as follows:Now how is that possible?

Solution to the so called Triangle Rearrangement or Disappearing Tile Puzzle (click here) :

It just looks as if the both the triangles are of same size, but actually they are not. There is only a slight difference in both the triangles which you tend to miss out even when you try them on paper cut outs, thinking that you were not perfect with cutting!!
The main difference comes in the inclined line of the triangle, i.e. the slope of the line.
The small change is slope is from 0.4 to 0.375. This small change is enough to accommodate the area of 1x1 area in the triangle.

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