Reasoning, convincing and proving

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

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

In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

What is the largest number Sophie can use to have seven positive integers with a mean of 7?

Can you find the areas of the trapezia in this sequence?

One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?

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

When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?

If it takes 852 digits to number all the pages of a book, what is the number of the last page?

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