Reasoning, convincing and proving

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
Squares in rectangles

Age

11 to 14

Challenge level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
problem
Semi-regular tessellations

Age

11 to 16

Challenge level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
Tessellating hexagons

Age

11 to 14

Challenge level

Which hexagons tessellate?
problem
Concrete wheel

Age

11 to 14

Challenge level

A huge wheel is rolling past your window. What do you see?
problem
Harmonic triangle

Age

14 to 16

Challenge level

Can you see how to build a harmonic triangle? Can you work out the next two rows?
problem
Triangle in a triangle

Age

14 to 16

Challenge level

Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
Odds and evens

Age

11 to 14

Challenge level

Are these games fair? How can you tell?
problem
Stringy quads

Age

7 to 11

Challenge level

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!