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!

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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?

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?

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

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

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

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?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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

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?

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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

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

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 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.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?

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?

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

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.

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?

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?

An environment which simulates working with Cuisenaire rods.

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.

You have 5 darts and your target score is 44. How many different ways could you score 44?

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!

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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!

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

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?

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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Here is a chance to play a version of the classic Countdown Game.

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

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

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?