Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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?

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?

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.

Read This Page

Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

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

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"?

Two and Two

Age 11 to 16 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Quadruple Sudoku

Age 11 to 16 Challenge Level:

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

Maths Trails

Age 7 to 14

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.

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!

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

Twin Line-swapping Sudoku

Age 14 to 16 Challenge Level:

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

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?

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.

Special Numbers

Age 11 to 14 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Football Sum

Age 11 to 14 Challenge Level:

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

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?

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.

Add to 200

Age 11 to 14 Challenge Level:

By selecting digits for an addition grid, what targets can you make?

Multiply the Addition Square

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?

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?

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?

Window Frames

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Charitable Pennies

Age 7 to 14 Challenge Level:

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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?

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".

Addition Equation Sudoku

Age 11 to 14 Challenge Level:

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

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?

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.

Ratio Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

More Children and Plants

Age 7 to 14 Challenge Level:

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

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.

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?

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.

Where Can We Visit?

Age 11 to 14 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?

Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

Another Quadruple Clue Sudoku

Age 11 to 16 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.

Intersection Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

Ratio Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

Peaches Today, Peaches Tomorrow...

Age 11 to 14 Challenge Level:

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

An Introduction to Magic Squares

Age 7 to 16

Find out about Magic Squares in this article written for students. Why are they magic?!

Rainstorm Sudoku

Age 14 to 16 Challenge Level:

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

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?

Ratio Sudoku 3

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

Quadruple Clue Sudoku

Age 11 to 16 Challenge Level:

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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.

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.

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.

Bochap Sudoku

Age 11 to 16 Challenge Level:

This Sudoku combines all four arithmetic operations.