Explaining, convincing and proving

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Which digit replaces x in this crossnumber?

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

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?

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

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

Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?