Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Instant Insanity

Age 11 to 18 Challenge Level:

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Cuboids

Age 11 to 14 Challenge Level:

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Tetrahedra Tester

Age 11 to 14 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Magic Caterpillars

Age 14 to 18 Challenge Level:

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

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?

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 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.

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.

Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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.

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.

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?

Corresponding Sudokus

Age 11 to 18

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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?

Reach 100

Age 7 to 14 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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?

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.

LOGO Challenge - Pentagram Pylons

Age 11 to 18 Challenge Level:

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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?

LOGO Challenge - Following On

Age 11 to 18 Challenge Level:

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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.

Product Sudoku

Age 11 to 16 Challenge Level:

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

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

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.

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.

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?

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?

Twin Line-swapping Sudoku

Age 14 to 16 Challenge Level:

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

Isosceles Triangles

Age 11 to 14 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Fence It

Age 11 to 14 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

An Introduction to Magic Squares

Age 7 to 16

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

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?

Difference Sudoku

Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku.

Shady Symmetry

Age 11 to 14 Challenge Level:

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

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.

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.

Football Sum

Age 11 to 14 Challenge Level:

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

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?

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.

Twin Chute-swapping Sudoku

Age 14 to 18 Challenge Level:

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Twin Corresponding Sudoku

Age 11 to 18 Challenge Level:

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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?

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?

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.

Squares in Rectangles

Age 11 to 14 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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?

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?

Pole Star Sudoku

Age 14 to 18 Challenge Level:

A Sudoku based on clues that give the differences between adjacent cells.

Alphabetti Sudoku

Age 11 to 16 Challenge Level:

This Sudoku requires you to do some working backwards before working forwards.