Factors and multiples

Can you fill in this table square? The numbers 2-12 were used to generate it with just one number used twice.

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Can you make square numbers by adding two prime numbers together?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.