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

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Intersection Sums Sudoku

Age 7 to 16 Challenge Level:

A Sudoku with clues given as sums of entries.

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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.

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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?

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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.

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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.

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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?

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Counters

Age 7 to 11 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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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.

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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.

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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.

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Arrangements

Age 7 to 11 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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More Transformations on a Pegboard

Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Cuboid-in-a-box

Age 7 to 11 Challenge Level:

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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Number Sandwiches

Age 7 to 14 Challenge Level:

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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Cereal Packets

Age 7 to 11 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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First Connect Three

Age 7 to 14 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?

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Tetrafit

Age 7 to 11 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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Junior Frogs

Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Triangle Edges

Age 5 to 7 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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Cuisenaire Counting

Age 5 to 7 Challenge Level:

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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A Bag of Marbles

Age 5 to 7 Challenge Level:

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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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?

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Combining Cuisenaire

Age 7 to 11 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

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Are You Well Balanced?

Age 5 to 7 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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Find the Difference

Age 5 to 7 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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Difference

Age 7 to 11 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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Fault-free Rectangles

Age 7 to 11 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

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A Square of Numbers

Age 7 to 11 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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Triangles All Around

Age 7 to 11 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

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Making Trains

Age 5 to 7 Challenge Level:

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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Red Even

Age 7 to 11 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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Same Length Trains

Age 5 to 7 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical?

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Three Ball Line Up

Age 5 to 7 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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The Third Dimension

Age 5 to 11 Challenge Level:

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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Code Breaker

Age 7 to 11 Challenge Level:

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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One to Fifteen

Age 7 to 11 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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Winning the Lottery

Age 7 to 11 Challenge Level:

Try out the lottery that is played in a far-away land. What is the chance of winning?

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Coloured Squares

Age 5 to 7 Challenge Level:

Use the clues to colour each square.

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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.

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Triangle Animals

Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Fair Exchange

Age 5 to 7 Challenge Level:

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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Making Cuboids

Age 7 to 11 Challenge Level:

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Growing Garlic

Age 5 to 7 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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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?

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First Connect Three for Two

Age 7 to 11 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.

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Multilink Cubes

Age 7 to 11 Challenge Level:

If you had 36 cubes, what different cuboids could you make?

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Seven Flipped

Age 7 to 11 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?