Explaining, convincing and proving

problem
Old order

Age

11 to 14

Challenge level

Who is the youngest in this family?
problem
Birthday party

Age

11 to 14

Challenge level

The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
problem
Wallpaper

Age

5 to 7

Challenge level

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
problem
Sizing them up

Age

5 to 7

Challenge level

Can you put these shapes in order of size? Start with the smallest.
problem
Trapezium four

Age

14 to 16

Challenge level

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
problem
Domino sorting

Age

5 to 7

Challenge level

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
problem
Integral inequality

Age

16 to 18

Challenge level

An inequality involving integrals of squares of functions.
problem
Integral sandwich

Age

16 to 18

Challenge level

Generalise this inequality involving integrals.
problem
Product Sudoku

Age

11 to 16

Challenge level

The clues for this Sudoku are the product of the numbers in adjacent squares.
problem
Litov's mean value theorem

Age

11 to 14

Challenge level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...