Being resilient

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Can you work out the probability of winning the Mathsland National Lottery?

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

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

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.

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you explain what is going on in these puzzling number tricks?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Can you create a Latin Square from multiples of a six digit number?