Copyright © University of Cambridge. All rights reserved.
Can you prove any of the things you've noticed from the main challenge are always true?
Instead of having a difference of two between the numbers showing on each face of the blue and the red dice, choose a new difference.
Now, what totals can you find? What do you notice? Explain what you notice.
Can you predict - without having to make them - what numbers need to be on the faces that you can see on the blue and the red dice to make a total of 42?
Are there more ways to make a total of 42?
Explain your reasoning.
What happens if you change the number of blue and red dice yet keep the structure the same? It must be a square and both sets of dice must still make triangles.
Can you make 42?
Explain your reasoning.
This problem featured in a preliminary round of the Young Mathematicians' Award 2014.