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problem

Diagonal Trace

7 to 11

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

problem

How Many Pieces?

5 to 7

How many loops of string have been used to make these patterns?

problem

Coin Lines

14 to 16

If a coin rolls and lands on a set of concentric circles what is the chance that the coin touches a line ?

problem

Two and One

5 to 7

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

problem

Rabbit Run

7 to 11

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

problem

Two Regular Polygons

14 to 16

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?