Explaining, convincing and proving

problem
Long list

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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?
problem
What's on the back?

Age

11 to 14

Challenge level

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?
problem
Ones, twos and threes

Age

11 to 14

Challenge level

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?
problem
Bookshop

Age

11 to 14

Challenge level

If Clara spends £23 on books and magazines, how many of each does she buy?
problem
Peter's primes

Age

14 to 16

Challenge level

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?
problem
Shaded square

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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