Challenge Level

Here is a game you could play with a friend...

Ask your friend to choose one of the shapes, and then try to identify which it is.

Your friend can only reply "Yes" or "No" to your questions.

Then swap over.

Isosceles trapezium |
Rectangle |
Rhombus |
Kite |

Parallelogram | Square | Trapezium | Arrowhead |

You may wish to print out this sheet to record the answers and help you eliminate possible shapes.

How many questions do you need to ask to

What would you ask first?

If your friend says "Yes", what would you ask next?

If your friend says "No", what would you ask next?

Charlie says he can

Which question might Charlie ask first? Which follow-up questions might he then ask?

Can you invent a game with more shapes, where you can always identify your friend's shape in four questions? What is the maximum number of shapes you could have in such a game?