Posing Questions and Making Conjectures - Advanced

Painting by Numbers

Stage: 5 Challenge Level: Challenge Level:1

How many different colours of paint would be needed to paint these pictures by numbers?

White Box

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Impossible Triangles?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these triangular jigsaws are impossible to finish?

The Clue Is in the Question

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Difference Dynamics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?