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?

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?

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?

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

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.

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?

Football Sum

Age 11 to 14
Challenge Level

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

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?

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.

Alphabetti Sudoku

Age 11 to 16
Challenge Level

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

Simultaneous Equations Sudoku

Age 11 to 16
Challenge Level

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

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?

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"?

Charitable Pennies

Age 7 to 14
Challenge Level

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

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?

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?

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.

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.

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.

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?

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?

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.

Tea Cups

Age 7 to 14
Challenge Level

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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...

A First Product Sudoku

Age 7 to 14
Challenge Level

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

Weights

Age 11 to 14
Challenge Level

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

Magic W

Age 14 to 16
Challenge Level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

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.

Ratio Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

Product Sudoku

Age 11 to 16
Challenge Level

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

Smith and Jones

Age 14 to 16
Challenge Level

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

Intersection Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with a twist.

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?

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.

Magnetic Personality

Age 7 to 16
Challenge Level

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Difference Sudoku

Age 14 to 16
Challenge Level

Use the differences to find the solution to this Sudoku.

Ratio Sudoku 3

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios or fractions.

Ratio Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

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?

An Introduction to Magic Squares

Age 7 to 16

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

More on Mazes

Age 7 to 14

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Making a Difference

Age 11 to 14
Challenge Level

How many different differences can you make?

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?

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.

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.

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?

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

Given the products of diagonally opposite 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.

Neighbourly Addition

Age 7 to 14
Challenge Level

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