Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Product Sudoku

Age 11 to 16 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

A First Product Sudoku

Age 11 to 14 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

Gabriel's Problem

Age 11 to 14 Challenge Level:

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

American Billions

Age 11 to 14 Challenge Level:

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Multiples Sudoku

Age 11 to 14 Challenge Level:

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Neighbourly Addition

Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Magic Vs

Age 7 to 11 Challenge Level:

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Number Detective

Age 5 to 11 Challenge Level:

Follow the clues to find the mystery number.

Sticky Dice

Age 7 to 11 Challenge Level:

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

A Mixed-up Clock

Age 7 to 11 Challenge Level:

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?

Read This Page

Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Two and Two

Age 11 to 16 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Cayley

Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

How Old Are the Children?

Age 11 to 14 Challenge Level:

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Alphabetti Sudoku

Age 11 to 16 Challenge Level:

This Sudoku requires you to do some working backwards before working forwards.

Multiply the Addition Square

Age 11 to 14 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Football Sum

Age 11 to 14 Challenge Level:

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

Star Product Sudoku

Age 11 to 16 Challenge Level:

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Pole Star Sudoku 2

Age 11 to 16 Challenge Level:

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

Shopping Basket

Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Peaches Today, Peaches Tomorrow...

Age 11 to 14 Challenge Level:

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

The Moons of Vuvv

Age 7 to 11 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Add to 200

Age 11 to 14 Challenge Level:

By selecting digits for an addition grid, what targets can you make?

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku?

Ben's Game

Age 11 to 16 Challenge Level:

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

An Introduction to Magic Squares

Age 7 to 16

Find out about Magic Squares in this article written for students. Why are they magic?!

Multiplication Squares

Age 7 to 11 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Curious Number

Age 7 to 11 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Mystery Matrix

Age 7 to 11 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Cinema Problem

Age 11 to 14 Challenge Level:

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Adding Plus

Age 7 to 11 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?

Neighbours

Age 7 to 11 Challenge Level:

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?

Spell by Numbers

Age 7 to 11 Challenge Level:

Can you substitute numbers for the letters in these sums?

Zargon Glasses

Age 7 to 11 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?

The Puzzling Sweet Shop

Age 5 to 11 Challenge Level:

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?

Tiling

Age 7 to 11 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

Ones Only

Age 11 to 14 Challenge Level:

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

Today's Date - 01/06/2009

Age 5 to 11 Challenge Level:

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

ABC

Age 7 to 11 Challenge Level:

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Two Egg Timers

Age 7 to 11 Challenge Level:

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?

How Much Did it Cost?

Age 7 to 11 Challenge Level:

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

Number Daisy

Age 11 to 14 Challenge Level:

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

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

Trebling

Age 7 to 11 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

One to Fifteen

Age 7 to 11 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Being Resourceful - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration.

Dart Target

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Prison Cells

Age 7 to 11 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?

Open Squares

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?