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 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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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
Here are some ideas to try in the classroom for using counters to investigate number patterns.
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
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?
Can you deduce the pattern that has been used to lay out these
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. . . .
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.
A fun game for two. You'll need some counters.
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?
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.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
An article for teachers which first appeared in the MA's Equals journal, featuring activities which use counters.