Exploring and noticing

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Which of these triangular jigsaws are impossible to finish?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Choose any three by three square of dates on a calendar page...

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.