1 out of 3
2 out of 3
1 out of 3
What on earth are polar coordinates, and why would you want to use them?
2 out of 3
Use vectors and matrices to explore the symmetries of crystals.
1 out of 3
Can you devise a fair scoring system when dice land edge-up or corner-up?
2 out of 3
Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?
2 out of 3
The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
1 out of 3
Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.
3 out of 3
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
