Explaining, convincing and proving

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?

Can you work out the values of J, M and C in this sum?

Weekly Problem 8 - 2016
Can you work out the size of the angles in a quadrilateral?

Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?

Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?

Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

Weekly Problem 38 - 2017
In the diagram, what is the value of $x$?