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. . . .
Which of these triangular jigsaws are impossible to finish?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
How many different colours of paint would be needed to paint these
pictures by numbers?
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?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.