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It Was 2010!

Stage: 1 and 2 Challenge Level:

If the answer's 2010, what could the question be?

Stage: 2 Challenge Level:

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Sometimes We Lose Things

Stage: 2 Challenge Level:

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Abundant Numbers

Stage: 2 Challenge Level:

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Exploring Number Patterns You Make

Stage: 2 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Calendar Patterns

Stage: 2 Challenge Level:

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Magic Constants

Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Number Squares

Stage: 1 and 2 Challenge Level:

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

Rocco's Race

Stage: 2 Short Challenge Level:

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Function Machines

Stage: 2 Challenge Level:

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Amy's Dominoes

Stage: 2 Challenge Level:

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Calendar Calculations

Stage: 2 Challenge Level:

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?

Four Goodness Sake

Stage: 2 Challenge Level:

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

The Money Maze

Stage: 2 Challenge Level:

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

Stage: 2 Challenge Level:

Use the information to work out how many gifts there are in each pile.

Book Codes

Stage: 2 Challenge Level:

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Sam's Quick Sum

Stage: 2 Challenge Level:

What is the sum of all the three digit whole numbers?

Oranges and Lemons

Stage: 2 Challenge Level:

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Polo Square

Stage: 2 Challenge Level:

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

Zargon Glasses

Stage: 2 Challenge Level:

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?

A-magical Number Maze

Stage: 2 Challenge Level:

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!

Back to School

Stage: 2 Challenge Level:

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Scoring with Dice

Stage: 2 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

How Many Eggs?

Stage: 2 Challenge Level:

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

On Target

Stage: 2 Challenge Level:

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

Hubble, Bubble

Stage: 2 Challenge Level:

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?

Highest and Lowest

Stage: 2 Challenge Level:

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Special 24

Stage: 2 Challenge Level:

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Arranging the Tables

Stage: 2 Challenge Level:

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.

Magic Squares 4x4

Stage: 2 Challenge Level:

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

Number Juggle

Stage: 2 Challenge Level:

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Buckets of Thinking

Stage: 2 Challenge Level:

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Napier's Bones

Stage: 2 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Penta Post

Stage: 2 Challenge Level:

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Stage: 2 Challenge Level:

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?

One Wasn't Square

Stage: 2 Challenge Level:

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

The Pied Piper of Hamelin

Stage: 2 Challenge Level:

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!

Clock Face

Stage: 2 Challenge Level:

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Prison Cells

Stage: 2 Challenge Level:

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?

Street Sequences

Stage: 1 and 2 Challenge Level:

Investigate what happens when you add house numbers along a street in different ways.

Cows and Sheep

Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

X Is 5 Squares

Stage: 2 Challenge Level:

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

Journeys in Numberland

Stage: 2 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Escape from the Castle

Stage: 2 Challenge Level:

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

How Old?

Stage: 2 Challenge Level:

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

Rabbits in the Pen

Stage: 2 Challenge Level:

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

Pouring the Punch Drink

Stage: 2 Challenge Level:

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.

Make 100

Stage: 2 Challenge Level:

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Zios and Zepts

Stage: 2 Challenge Level:

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?