Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Factor Lines

Age 7 to 14
Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.

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?"

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

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?

Twin Corresponding Sudoku III

Age 11 to 16
Challenge Level

Two sudokus in one. Challenge yourself to make the necessary connections.

Build it Up

Age 7 to 11
Challenge Level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Multiples Sudoku

Age 11 to 14
Challenge Level

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

Twin Corresponding Sudokus II

Age 11 to 16
Challenge Level

Two sudokus in one. Challenge yourself to make the necessary connections.

Cuboids

Age 11 to 14
Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Intersection Sums Sudoku

Age 7 to 16
Challenge Level

A Sudoku with clues given as sums of entries.

Wallpaper Sudoku

Age 11 to 16
Challenge Level

A Sudoku that uses transformations as supporting clues.

Latin Lilies

Age 7 to 14
Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

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.

Waiting for Blast Off

Age 7 to 11
Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Button-up Some More

Age 7 to 11
Challenge Level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Number Sandwiches

Age 7 to 14
Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?

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?

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 7 to 14
Challenge Level

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

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.

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.

Counters

Age 7 to 11
Challenge Level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Twinkle Twinkle

Age 7 to 14
Challenge Level

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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...

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.

Plates of Biscuits

Age 7 to 11
Challenge Level

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

School Fair Necklaces

Age 5 to 11
Challenge Level

How many possible necklaces can you find? And how do you know you've found them all?

Extra Challenges from Madras

Age 11 to 14
Challenge Level

A few extra challenges set by some young NRICH members.

Creating Cubes

Age 7 to 11
Challenge Level

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Stairs

Age 5 to 11
Challenge Level

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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.

Integrated Sums Sudoku

Age 11 to 16
Challenge Level

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

An Introduction to Magic Squares

Age 7 to 16

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

Magic Potting Sheds

Age 11 to 14
Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Painting Possibilities

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Ribbon Squares

Age 7 to 11
Challenge Level

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

Map Folding

Age 7 to 11
Challenge Level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Finding All Possibilities Upper Primary

Age 7 to 11
Challenge Level

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Code Breaker

Age 7 to 11
Challenge Level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Triangles to Tetrahedra

Age 11 to 14
Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Making a Difference

Age 11 to 14
Challenge Level

How many different differences can you make?

Sums and Differences 1

Age 7 to 11
Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Centred Squares

Age 7 to 11
Challenge Level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Colour in the Square

Age 7 to 16
Challenge Level

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Ratio Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.