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Resources tagged with Working systematically similar to Changing Places:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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One Out One Under

Age 14 to 16 Challenge Level:

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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Instant Insanity

Age 11 to 18 Challenge Level:

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

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

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Ratio Sudoku 3

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

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You Owe Me Five Farthings, Say the Bells of St Martin's

Age 11 to 14 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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Ratio Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

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Wallpaper Sudoku

Age 11 to 16 Challenge Level:

A Sudoku that uses transformations as supporting clues.

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Corresponding Sudokus

Age 11 to 18

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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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?

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Intersection Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

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Pole Star Sudoku

Age 14 to 18 Challenge Level:

A Sudoku based on clues that give the differences between adjacent cells.

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Diagonal Sums Sudoku

Age 7 to 16 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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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.

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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.

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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?

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Twin Corresponding Sudokus II

Age 11 to 16 Challenge Level:

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

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Twin Corresponding Sudoku III

Age 11 to 16 Challenge Level:

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

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Tetrahedra Tester

Age 11 to 14 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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Twin Corresponding Sudoku

Age 11 to 18 Challenge Level:

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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Ratio Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

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Intersection Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

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When Will You Pay Me? Say the Bells of Old Bailey

Age 11 to 14 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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Intersection Sums Sudoku

Age 7 to 16 Challenge Level:

A Sudoku with clues given as sums of entries.

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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.

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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.

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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.

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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?

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Quadruple Sudoku

Age 11 to 16 Challenge Level:

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

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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?

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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?

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LOGO Challenge - Triangles-squares-stars

Age 11 to 16 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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Olympic Magic

Age 14 to 16 Challenge Level:

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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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?

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Squares in Rectangles

Age 11 to 14 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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First Connect Three for Two

Age 7 to 14 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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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.

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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".

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Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

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A First Product Sudoku

Age 11 to 14 Challenge Level:

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

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The Naked Pair in Sudoku

Age 7 to 16

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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Peaches Today, Peaches Tomorrow...

Age 11 to 14 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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Coins

Age 11 to 14 Challenge Level:

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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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?

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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?

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Difference Dynamics

Age 14 to 18 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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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!

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Shady Symmetry

Age 11 to 14 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares?

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Ben's Game

Age 11 to 14 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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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.

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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.