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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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....?

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?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Can you find all the different ways of lining up these Cuisenaire rods?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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 the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.

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

Investigate the different ways you could split up these rooms so that you have double the number.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

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

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

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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?

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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

In how many ways can you stack these rods, following the rules?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

In this matching game, you have to decide how long different events take.

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?

This dice train has been made using specific rules. How many different trains can you make?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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?

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?