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

Problem Solving, Using and Applying and Functional Mathematics

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

Stage: 3 and 4 Challenge Level:

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

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?

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.

Difference Sudoku

Stage: 3 and 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

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.

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.

Pole Star Sudoku 2

Stage: 3 and 4 Challenge Level:

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

One Out One Under

Stage: 4 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?

Gr8 Coach

Stage: 3 Challenge Level:

Can you coach your rowing eight to win?

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?

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?

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?

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

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

Magic Caterpillars

Stage: 4 and 5 Challenge Level:

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Crossing the Town Square

Stage: 2 and 3 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

The Naked Pair in Sudoku

Stage: 2, 3 and 4

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

Olympic Logic

Stage: 3 and 4 Challenge Level:

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

Stage: 3 Challenge Level:

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

Twin Corresponding Sudokus II

Stage: 3 and 4 Challenge Level:

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

Factors and Multiple Challenges

Stage: 3 Challenge Level:

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Spot the Card

Stage: 4 Challenge 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?

Masterclass Ideas: Working Systematically

Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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. . . .

Ratio Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

LOGO Challenge - Sequences and Pentagrams

Stage: 3, 4 and 5 Challenge Level:

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Cinema Problem

Stage: 3 and 4 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.

Magnetic Personality

Stage: 2, 3 and 4 Challenge Level:

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Latin Squares

Stage: 3, 4 and 5

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

Intersection Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Seasonal Twin Sudokus

Stage: 3 and 4 Challenge Level:

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

Stage: 3, 4 and 5 Challenge Level:

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

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 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?

Colour Islands Sudoku

Stage: 3 Challenge Level:

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

Difference Dynamics

Stage: 4 and 5 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?

Sociable Cards

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

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

Where Can We Visit?

Stage: 3 Challenge Level:

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Stage: 3 Challenge 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?

Bent Out of Shape

Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

Inky Cube

Stage: 2 and 3 Challenge 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?

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.

More Children and Plants

Stage: 2 and 3 Challenge Level:

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

I've Submitted a Solution - What Next?

Stage: 1, 2, 3, 4 and 5

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

Stage: 3, 4 and 5 Challenge Level:

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Rainstorm Sudoku

Stage: 4 Challenge Level:

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

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.

Stage: 3 and 4 Challenge 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.

Multiplication Equation Sudoku

Stage: 4 and 5 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.

Weights

Stage: 3 Challenge Level:

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