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T puzzle

By David, 9 October 2015 Activity

Atriangle, two quadrilaterals and a pentagon.

Cut out the pieces of the puzzle

There’s only four pieces, but this puzzle is Totally Tricky!

You will need

What to do

  1. Cut out the four pieces.
  2. Rearrange them so they make a capital T shape.
    A capital T shape

    Rearrange the pieces to make this shape

Tips

  1. Don’t give up!
  2. Try drawing a T shape. Make it as close to the answer as you can imagine.
  3. Think about all the corners a T shape has. You’re going to need lots of right angles.
  4. Do any of your pieces have special angles?
  5. The funny 5-sided shape is very important. You don’t have to fill the hole in it.
    A T that is much wider than it is tall.

    You can also make a short, fat T shape

  6. One of the pieces has to go ‘diagonally’.

What’s happening?

This conundrum has been puzzling people for over a century. A scientific study found that most university students could not solve the puzzle in 15 minutes, and they needed hints to finish it.

There are a few things that people often get wrong with this puzzle. It is very tempting to fill the gap in the 5-sided piece. The gap is a right angle and each of the other pieces will fit in there. But the gap is a red herring. You have to leave it empty to solve the puzzle.

People also want to put all the pieces running left to right, or up and down. A T shape is made of horizontal and vertical lines, but in order to solve the puzzle the 5-sided piece needs to be on a 45° angle.

The 5-sided shape is the key piece. When a group of students were given this puzzle with the 5-sided shape in the right place they all solved the puzzle in minutes. Without this hint, the puzzle usually takes a lot longer. Famous mathematical journalist Martin Gardner once said, “I know of no polygon-dissection puzzle with as few pieces that is so intractable.”

More information
View the solution

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