Reasoning, convincing and proving

problem
Multiplication arithmagons

Age

14 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
problem
Reversals

Age

11 to 14

Challenge level

Where should you start, if you want to finish back where you started?
problem
Pythagoras perimeters

Age

14 to 16

Challenge level

If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Difference of two squares

Age

14 to 16

Challenge level

What is special about the difference between squares of numbers adjacent to multiples of three?
problem
Impossibilities

Age

11 to 14

Challenge level

Just because a problem is impossible doesn't mean it's difficult...
problem
Perimeter challenge

Age

11 to 14

Challenge level

Can you deduce the perimeters of the shapes from the information given?
problem
Cryptarithms

Age

11 to 14

Challenge level

Can you crack these cryptarithms?
problem
Overlaps

Age

11 to 14

Challenge level

Can you find ways to put numbers in the overlaps so the rings have equal totals?
problem
Quadrilaterals in a square

Age

11 to 14

Challenge level

What's special about the area of quadrilaterals drawn in a square?
problem
Triangles in a square

Age

11 to 14

Challenge level

What are the possible areas of triangles drawn in a square?