Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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?

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.

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?

Sticky Numbers

Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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?

Alphabetti Sudoku

Age 11 to 16 Challenge Level:

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

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?

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.

Tiling

Age 7 to 11 Challenge Level:

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

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?"

Neighbourly Addition

Age 7 to 14 Challenge Level:

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

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?

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"?

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?

A Square Deal

Age 7 to 11 Challenge Level:

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

A Right Charlie

Age 7 to 11 Challenge Level:

Can you use this information to work out Charlie's house number?

An Introduction to Magic Squares

Age 7 to 16

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

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?

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

Seven Flipped

Age 7 to 11 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Integrated Product Sudoku

Age 11 to 16 Challenge Level:

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

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

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?

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.

Add to 200

Age 11 to 14 Challenge Level:

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

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?

Charitable Pennies

Age 7 to 14 Challenge Level:

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Building with Rods

Age 7 to 11 Challenge Level:

In how many ways can you stack these rods, following the rules?

Seven Pots of Plants

Age 7 to 11 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Weights

Age 11 to 14 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Money Bags

Age 5 to 11 Challenge Level:

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?

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?

All the Digits

Age 7 to 11 Challenge Level:

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Palindromic Date

Age 7 to 11 Challenge Level:

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Ancient Runes

Age 7 to 11 Challenge Level:

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Symmetry Challenge

Age 7 to 11 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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?

A First Product Sudoku

Age 11 to 14 Challenge Level:

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

Plate Spotting

Age 7 to 11 Challenge Level:

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Advent Sudoku

Age 11 to 14 Challenge Level:

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Family Tree

Age 7 to 11 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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...

Addition Equation Sudoku

Age 11 to 14 Challenge Level:

You need to find the values of the stars before you can apply normal Sudoku rules.

All Seated

Age 7 to 11 Challenge Level:

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?

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.

Seasonal Twin Sudokus

Age 11 to 16 Challenge Level:

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?

Polo Square

Age 7 to 11 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.

Quadruple Sudoku

Age 11 to 16 Challenge Level:

Four small numbers give the clue to the contents of the four surrounding cells.