Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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?

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.

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

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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.

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?

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

What happens when you try and fit the triomino pieces into these two grids?

Find out what a "fault-free" rectangle is and try to make some of your own.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

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

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

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 different rhythms can you make by putting two drums on the wheel?

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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

My coat has three buttons. How many ways can you find to do up all the buttons?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.