Exploring and noticing

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.

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

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?