Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Spot the Card

Age 14 to 16Challenge Level

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Colour in the Square

Age 7 to 16Challenge 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?

Window Frames

Age 5 to 14Challenge Level

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

Number Sandwiches

Age 7 to 14Challenge Level

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

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.

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 16Challenge 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. . . .

One Out One Under

Age 14 to 16Challenge 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?

Intersection Sudoku 2

Age 11 to 16Challenge Level

A Sudoku with a twist.

Twinkle Twinkle

Age 7 to 14Challenge 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.

Magic Potting Sheds

Age 11 to 14Challenge 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?

More Magic Potting Sheds

Age 11 to 14Challenge 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?

Factor Lines

Age 7 to 14Challenge Level

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

Twin Corresponding Sudokus II

Age 11 to 16Challenge Level

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

Intersection Sudoku 1

Age 11 to 16Challenge Level

A Sudoku with a twist.

Seasonal Twin Sudokus

Age 11 to 16Challenge Level

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

Age 11 to 14Challenge Level

A few extra challenges set by some young NRICH members.

Age 11 to 14Challenge Level

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

LOGO Challenge - Triangles-squares-stars

Age 11 to 16Challenge 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.

Teddy Town

Age 5 to 14Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Ratio Sudoku 3

Age 11 to 16Challenge Level

A Sudoku with clues as ratios or fractions.

Diagonal Product Sudoku

Age 11 to 16Challenge Level

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

Ratio Sudoku 1

Age 11 to 16Challenge Level

A Sudoku with clues as ratios.

Ratio Sudoku 2

Age 11 to 16Challenge Level

A Sudoku with clues as ratios.

Wallpaper Sudoku

Age 11 to 16Challenge Level

A Sudoku that uses transformations as supporting clues.

Intersection Sums Sudoku

Age 7 to 16Challenge Level

A Sudoku with clues given as sums of entries.

Bochap Sudoku

Age 11 to 16Challenge Level

This Sudoku combines all four arithmetic operations.

Diagonal Sums Sudoku

Age 7 to 16Challenge Level

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

Rectangle Outline Sudoku

Age 11 to 16Challenge Level

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Twin Corresponding Sudoku III

Age 11 to 16Challenge Level

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

Olympic Magic

Age 14 to 16Challenge 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?

Rainstorm Sudoku

Age 14 to 16Challenge Level

Use the clues about the shaded areas to help solve this sudoku

Latin Lilies

Age 7 to 14Challenge Level

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

Age 11 to 16Challenge 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.

Sociable Cards

Age 11 to 14Challenge Level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Weights

Age 11 to 14Challenge Level

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

Age 11 to 14Challenge Level

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

The Best Card Trick?

Age 11 to 16Challenge Level

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Age 11 to 14Challenge Level

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

Inky Cube

Age 7 to 14Challenge 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?

Smith and Jones

Age 14 to 16Challenge 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!

Magic W

Age 14 to 16Challenge 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.

Gabriel's Problem

Age 11 to 14Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Age 11 to 14Challenge 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?

Sticky Numbers

Age 11 to 14Challenge Level

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

Making a Difference

Age 11 to 14Challenge Level

How many different differences can you make?

Cinema Problem

Age 11 to 14Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

LOGO Challenge - the Logic of LOGO

Age 11 to 16Challenge Level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Making Maths: Double-sided Magic Square

Age 7 to 14Challenge Level

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

Peaches Today, Peaches Tomorrow...

Age 11 to 14Challenge 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?