Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

If you have only four weights, where could you place them in order to balance this equaliser?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Find all the numbers that can be made by adding the dots on two dice.

Can you hang weights in the right place to make the equaliser balance?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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

Can you use the information to find out which cards I have used?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Use these four dominoes to make a square that has the same number of dots on each side.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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.

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

Number problems at primary level that require careful consideration.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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.

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?