# Resources tagged with: Working systematically

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### There are 131 results

Broad Topics > Thinking Mathematically > Working systematically

### Summing Consecutive Numbers

##### Age 11 to 14Challenge 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?

### Tea Cups

##### Age 7 to 14Challenge 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.

### 9 Weights

##### Age 11 to 14Challenge 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?

### Oranges and Lemons, Say the Bells of St Clement's

##### Age 11 to 14Challenge Level

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

### The Great Weights Puzzle

##### Age 14 to 16Challenge 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?

### 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?

### Making a Difference

##### Age 11 to 14Challenge Level

How many different differences can you make?

### Star Product Sudoku

##### Age 11 to 16Challenge 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.

### Twin Line-swapping Sudoku

##### Age 14 to 16Challenge Level

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

##### Age 11 to 14Challenge 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

### Colour Islands Sudoku

##### Age 11 to 14Challenge Level

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

### 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.

##### 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.

### 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?

### Pole Star Sudoku 2

##### Age 11 to 16Challenge Level

This Sudoku, based on differences. Using the one clue number can you find the solution?

### Consecutive Negative Numbers

##### Age 11 to 14Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

### 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.

##### 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".

##### Age 11 to 14Challenge Level

A few extra challenges set by some young NRICH members.

### Intersection Sudoku 2

##### Age 11 to 16Challenge Level

A Sudoku with a twist.

### 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?

### Counting on Letters

##### Age 11 to 14Challenge Level

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

### Ratio Sudoku 2

##### Age 11 to 16Challenge Level

A Sudoku with clues as ratios.

### 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.

##### Age 11 to 16Challenge Level

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

### Special Numbers

##### Age 11 to 14Challenge 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?

### Integrated Product Sudoku

##### Age 11 to 16Challenge 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.

##### Age 11 to 16Challenge 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.

### 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.

##### Age 11 to 14Challenge Level

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

### Alphabetti Sudoku

##### Age 11 to 16Challenge Level

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

### 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.

### Olympic Logic

##### Age 11 to 16Challenge Level

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

### Crossing the Bridge

##### Age 11 to 14Challenge Level

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

### Number Daisy

##### Age 11 to 14Challenge 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?

### 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?

### 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?

### Charitable Pennies

##### Age 7 to 14Challenge Level

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

### Coins

##### Age 11 to 14Challenge Level

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

### Simultaneous Equations Sudoku

##### Age 11 to 16Challenge Level

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

##### 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?

### Rainstorm Sudoku

##### Age 14 to 16Challenge Level

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

### 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.

### 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.

### How Old Are the Children?

##### Age 11 to 14Challenge 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?"

### Ones Only

##### Age 11 to 14Challenge Level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

### Window Frames

##### Age 5 to 14Challenge Level

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

### 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?