Can you find the chosen number from the grid using the clues?

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.

What two-digit numbers can you make with these two dice? What can't you make?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Find out about Magic Squares in this article written for students. Why are they magic?!

Can you replace the letters with numbers? Is there only one solution in each case?

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

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

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?

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

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake 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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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?

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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?

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