Resources tagged with: Working systematically

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

Tea Cups

Age 7 to 14 Challenge 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.

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.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 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.

How Old Are the Children?

Age 11 to 14 Challenge 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?"

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?

Star Product Sudoku

Age 11 to 16 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.

LCM Sudoku

Age 14 to 16 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Twin Line-swapping Sudoku

Age 14 to 16 Challenge Level:

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

Number Daisy

Age 11 to 14 Challenge 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 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?

LCM Sudoku II

Age 11 to 18 Challenge Level:

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Pole Star Sudoku 2

Age 11 to 16 Challenge Level:

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

Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

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.

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?

More Children and Plants

Age 7 to 14 Challenge Level:

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

Crossing the Bridge

Age 11 to 14 Challenge Level:

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

More Plant Spaces

Age 7 to 14 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.

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

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

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?

Age 11 to 16 Challenge Level:

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

LOGO Challenge - the Logic of LOGO

Age 11 to 16 Challenge 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?

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?

LOGO Challenge - Sequences and Pentagrams

Age 11 to 18 Challenge Level:

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

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?

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.

Ratio Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

Latin Squares

Age 11 to 18

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.

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!

Age 11 to 14 Challenge Level:

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

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".

A First Product Sudoku

Age 11 to 14 Challenge Level:

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

Weights

Age 11 to 14 Challenge Level:

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

Teddy Town

Age 5 to 14 Challenge 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?

Intersection Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

Colour Islands Sudoku

Age 11 to 14 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.

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?

Twin Corresponding Sudoku III

Age 11 to 16 Challenge Level:

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

Latin Lilies

Age 7 to 16 Challenge Level:

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Building with Longer Rods

Age 7 to 14 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

I've Submitted a Solution - What Next?

Age 5 to 18

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

Inky Cube

Age 7 to 14 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?

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?

Age 11 to 14 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?

Rainstorm Sudoku

Age 14 to 16 Challenge Level:

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

Rectangle Outline Sudoku

Age 11 to 16 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.

Multiples Sudoku

Age 11 to 14 Challenge Level:

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

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.

Colour Islands Sudoku 2

Age 11 to 18 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.