A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

This task follows on from Build it Up and takes the ideas into three dimensions!

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Can you find all the different triangles on these peg boards, and find their angles?

How many different triangles can you make on a circular pegboard that has nine pegs?