ඉතුරු කෑල්ලට මොකද උනේ ???

රූප සටහනේ දැක්වෙන රූප දෙකම නිර්මාණය කරලා තියෙන්නෙ එකම තල රූප කොටස් යොදාගෙන. ඒත් රූප දෙක වර්ගඵලයෙන් සමාන වෙන්නෙ නෑ. ඇත්තටම මේක වෙන්න පුලුවන්ද ???

නෑ... ඇත්තටම මෙතනදි රැවටෙන්නෙ අපිමයි..

Solution

The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, because what appears to be the hypotenuse is bent. In other words, the "hypotenuse" does not maintain a consistent slope, even though it may appear that way to the human eye.

A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be ${\displaystyle \textstyle {S={\frac {13\times 5}{2}}=32.5}}$(13x5)/2 = 32.5 units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent. With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square.
The amount of bending is approximately 1/28th of a unit (1.245364267°), which is difficult to see on the diagram of the puzzle, and was illustrated as a graphic. Note the grid point where the red and blue triangles in the lower image meet (5 squares to the right and two units up from the lower left corner of the combined figure), and compare it to the same point on the other figure; the edge is slightly under the mark in the upper image, but goes through it in the lower. Overlaying the hypotenuses from both figures results in a very thin parallelogram (represented with the four red dots) with an area of exactly one grid square, so the "missing" area.