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

Pair Sums

Stage: 3 Challenge Level:

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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. . . .

Magic Potting Sheds

Stage: 3 Challenge 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?

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.

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?

How Old Are the Children?

Stage: 3 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?"

Ones Only

Stage: 3 Challenge Level:

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

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?

Medal Muddle

Stage: 3 Challenge Level:

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

Football Sum

Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

First Connect Three

Stage: 2, 3 and 4 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Integrated Product Sudoku

Stage: 3 and 4 Challenge 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.

A First Product Sudoku

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Constellation Sudoku

Stage: 4 and 5 Challenge Level:

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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.

Consecutive Negative Numbers

Stage: 3 Challenge Level:

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

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.

Rainstorm Sudoku

Stage: 4 Challenge Level:

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

A Long Time at the Till

Stage: 4 and 5 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

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

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.

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 and 4 Challenge Level:

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

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?

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".

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?

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?

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

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.

Magic W

Stage: 4 Challenge 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.

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?

Weights

Stage: 3 Challenge Level:

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

Product Sudoku

Stage: 3, 4 and 5 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

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.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

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

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?

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.

Bochap Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku combines all four arithmetic operations.

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

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

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.

Twin Corresponding Sudoku III

Stage: 3 and 4 Challenge Level:

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

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. . . .

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.

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. . . .

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.