What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Use the ratio of cashew nuts to peanuts to find out how many peanuts Rachel has. What would the ratio be if Rachel and Marianne mixed their bags?

Can you deduce the pattern that has been used to lay out these bottle tops?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

An article for teachers which first appeared in the MA's Equals journal, featuring activities which use counters.