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by:  Erik Oosterwal

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The Disappearing Tile - Solution

If you were to cut out the shapes from the upper figure on the previous page and lay them over the triangle in the lower figure you'll find they don't quite match up equally...


The slopes of the two triangles are slightly different.  The slope of the smaller triangle is 2/5 or 0.4 while the slope of the larger triangle is 3/8 or 0.375.  The slope of the entire figure is 5/13 or 0.38461...  We're led to believe that the slopes are equal, but in reality the slope of the upper figure is bowing in slightly, and the slope of the lower figure is bowing out slightly.  The difference between them is enough to equal the area of a 1x1 square.

All original puzzles and solutions are © Erik Oosterwal 1993-2008

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