Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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?

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?

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

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"?

Special Numbers

Age 11 to 14
Challenge Level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Charitable Pennies

Age 7 to 14
Challenge Level

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

Add to 200

Age 11 to 14
Challenge Level

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

Alphabetti Sudoku

Age 11 to 16
Challenge Level

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

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.

Football Sum

Age 11 to 14
Challenge Level

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

Weights

Age 11 to 14
Challenge Level

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

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?

Colour Islands Sudoku

Age 11 to 14
Challenge Level

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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?

Summing Consecutive Numbers

Age 11 to 14
Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

More Magic Potting Sheds

Age 11 to 14
Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Making a Difference

Age 11 to 14
Challenge Level

How many different differences can you make?

An Introduction to Magic Squares

Age 7 to 16

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

Difference Sudoku

Age 14 to 16
Challenge Level

Use the differences to find the solution to this Sudoku.

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.

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

Product Sudoku

Age 11 to 16
Challenge Level

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

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.

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...

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.

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?

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.

LCM Sudoku

Age 14 to 16
Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Simultaneous Equations Sudoku

Age 11 to 16
Challenge Level

Solve the equations to identify the clue numbers in this Sudoku problem.

The Great Weights Puzzle

Age 14 to 16
Challenge Level

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Window Frames

Age 5 to 14
Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

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.

Pair Sums

Age 11 to 14
Challenge Level

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

A First Product Sudoku

Age 7 to 14
Challenge Level

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

Multiples Sudoku

Age 11 to 14
Challenge Level

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

Making Maths: Double-sided Magic Square

Age 7 to 14
Challenge Level

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?"

Another Quadruple Clue Sudoku

Age 11 to 16
Challenge Level

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

9 Weights

Age 11 to 14
Challenge Level

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Where Can We Visit?

Age 11 to 14
Challenge Level

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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".

Quadruple Clue Sudoku

Age 11 to 16
Challenge Level

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

Latin Lilies

Age 7 to 16
Challenge Level

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Olympic Logic

Age 11 to 16
Challenge Level

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Inky Cube

Age 7 to 14
Challenge Level

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?

Twin Line-swapping Sudoku

Age 14 to 16
Challenge Level

A pair of Sudoku puzzles that together lead to a complete solution.