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#### Resources tagged with Working systematically similar to Like a Circle in a Spiral:

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

### Introducing NRICH TWILGO

##### Stage: 1, 2, 3, 4 and 5 Challenge Level:

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### LOGO Challenge - Triangles-squares-stars

##### Stage: 3 and 4 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.

### A Square of Numbers

##### Stage: 2 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

### Ratio Sudoku 3

##### Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

### More Plant Spaces

##### Stage: 2 and 3 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

##### Stage: 3 and 4 Challenge Level:

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

### Intersection Sudoku 1

##### Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

### Shaping Up

##### Stage: 2 Challenge Level:

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

### Ratio Sudoku 2

##### Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

### 9 Weights

##### Stage: 3 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?

### Corresponding Sudokus

##### Stage: 3, 4 and 5

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

### Diagonal Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

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

### Home City

##### Stage: 2 Challenge Level:

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

### Colour Islands Sudoku 2

##### Stage: 3, 4 and 5 Challenge Level:

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

### Triangles All Around

##### Stage: 2 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

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

##### Stage: 3 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?

### Junior Frogs

##### Stage: 2 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

### More Transformations on a Pegboard

##### Stage: 2 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

### Colour in the Square

##### Stage: 2 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?

### Product Sudoku 2

##### Stage: 3 and 4 Challenge Level:

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

### More Children and Plants

##### Stage: 2 and 3 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

### Red Even

##### Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

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

### More Magic Potting Sheds

##### Stage: 3 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?

### Isosceles Triangles

##### Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Team Scream

##### Stage: 2 Challenge Level:

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

### Maths Trails

##### Stage: 2 and 3

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.

### Sticky Numbers

##### Stage: 3 Challenge Level:

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

### More on Mazes

##### Stage: 2 and 3

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.

### Twin Corresponding Sudokus II

##### Stage: 3 and 4 Challenge Level:

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

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

### Rectangle Outline Sudoku

##### Stage: 3 and 4 Challenge 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.

### Integrated Sums Sudoku

##### Stage: 3 and 4 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. . . .

### Winning the Lottery

##### Stage: 2 Challenge Level:

Try out the lottery that is played in a far-away land. What is the chance of winning?

### Intersection Sudoku 2

##### Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

### Combining Cuisenaire

##### Stage: 2 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

### Twinkle Twinkle

##### Stage: 2 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.

### Product Doubles Sudoku

##### Stage: 3 and 4 Challenge Level:

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

### Twin Corresponding Sudoku III

##### Stage: 3 and 4 Challenge Level:

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

### Arrangements

##### Stage: 2 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

### Counting on Letters

##### Stage: 3 Challenge 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?

### Sandwiches

##### Stage: 2, 3, 4 and 5 Challenge Level:

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

### Tetrafit

##### Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

### How Long Does it Take?

##### Stage: 2 Challenge Level:

In this matching game, you have to decide how long different events take.

### Counters

##### Stage: 2 Challenge Level:

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

### Difference

##### Stage: 2 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

### Dicey Perimeter, Dicey Area

##### Stage: 2 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

##### Stage: 3 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?

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

##### Stage: 3 Challenge Level:

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