Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > 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.

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.

Consecutive Numbers

Age 7 to 14 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Counting on Letters

Age 11 to 14 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?

Plants

Age 5 to 14 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Twin Line-swapping Sudoku

Age 14 to 16 Challenge Level:

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

Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

Quadruple Sudoku

Age 11 to 16 Challenge Level:

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

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.

Medal Muddle

Age 11 to 14 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?

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?

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?

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?

The Great Weights Puzzle

Age 14 to 16 Challenge 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?

Binomial Coefficients

Age 14 to 18

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

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?

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.

Building with Longer Rods

Age 7 to 14 Challenge Level:

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

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.

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?

Extra Challenges from Madras

Age 11 to 14 Challenge Level:

A few extra challenges set by some young NRICH members.

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?

Wallpaper Sudoku

Age 11 to 16 Challenge Level:

A Sudoku that uses transformations as supporting clues.

Magic W

Age 14 to 16 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.

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?

Advent Sudoku

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".

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.

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?

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?

Twin Corresponding Sudokus II

Age 11 to 16 Challenge Level:

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

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.

Colour in the Square

Age 7 to 16 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?

Bochap Sudoku

Age 11 to 16 Challenge Level:

This Sudoku combines all four arithmetic operations.

Making Maths: Double-sided Magic Square

Age 7 to 14 Challenge Level:

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

Twin Corresponding Sudoku III

Age 11 to 16 Challenge Level:

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

Rainstorm Sudoku

Age 14 to 16 Challenge Level:

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

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?

Constellation Sudoku

Age 14 to 18 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.

Summing Consecutive Numbers

Age 11 to 14 Challenge 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?

Olympic Magic

Age 14 to 16 Challenge Level:

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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?

One Out One Under

Age 14 to 16 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?

Twinkle Twinkle

Age 7 to 14 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.

Spot the Card

Age 14 to 16 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?

Advent Calendar 2011 - Secondary

Age 11 to 18 Challenge Level:

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

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.

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?

Cayley

Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?