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

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

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

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

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This Sudoku, based on differences. Using the one clue number can you find the solution?

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

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

This challenge extends the Plants investigation so now four or more children are involved.

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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?

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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?

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

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?

These two group activities use mathematical reasoning - one is numerical, one geometric.

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.

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?

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!

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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?

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.

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?

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Can you make square numbers by adding two prime numbers together?

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?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.

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?

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?

A game for 2 players. Practises subtraction or other maths operations knowledge.

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