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

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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?

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

Which of these triangular jigsaws are impossible to finish?

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?

Weekly Problem 37 - 2014

Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.

Weekly Problem 46 - 2011

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Weekly Problem 28 - 2014

What is the units digit of the given expression?

Weekly Problem 30 - 2014

What is the value of $2006 \times 2008 - 2007 \times 2007$?