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T puzzle

By David Shaw, 9 October 2015

Cut out the pieces of the puzzle

You will need

• Scissors
• A printout of the T-puzzle template

What to do

1. Cut out the four pieces.
2. Rearrange them so they make 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.
   

   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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