Being resilient

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Can you make sense of the three methods to work out what fraction of the total area is shaded?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

Can you use the information to find out which cards I have used?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Which numbers can we write as a sum of square numbers?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

What could the half time scores have been in these Olympic hockey matches?