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?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Number problems at primary level that require careful consideration.

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?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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?

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?

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?

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

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?

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

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.

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?

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

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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

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

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

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?

An activity making various patterns with 2 x 1 rectangular tiles.

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.

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?

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

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