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?

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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?

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?

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?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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

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!

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

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?

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 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?

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.

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?

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

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

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

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?

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

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?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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?

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.

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?

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

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?

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

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?

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?