Square-Triangle and T Puzzles

Square-Triangle: Can you combine the four green pieces to form a square?

Square-Triangle: Can you combine the four green pieces to form an equilateral triangle?

The T: Can you combine the four yellow pieces form a big T? Hint: How is the right angle used? What other shapes can you make? Can you make an arrowhead?

The square-triangle puzzle is an example of a dissection problem. The idea is to start with one shape, then cut it up into pieces that can be rearranged to make another shape. In this case, if we start with an equilateral triangle, how can we make it into a square using three cuts. The solution is the square-triangle puzzle. We can move between the two solutions if we imagine the pieces on hinges.

It is not known if we can turn an equilateral triangle into a square using three pieces.

The T puzzle consists of four tiles that combine to make a capital T. Although the puzzle only has four pieces, it is very difficult to see the solution. The difficulty comes from the strange 5-sided tile. This tile contains a right-angle, and so it is very tempting to try to fill that notch with one of the other pieces. However, the right-angle is an external angle, where the horizontal and vertical lines of a T meet, and should not be filled.