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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Consecutive Negative Numbers

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Special Numbers

Stage: 3 Challenge Level: Challenge Level:1

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?

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Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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Maths Trails

Stage: 2 and 3

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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9 Weights

Stage: 3 Challenge Level: Challenge Level:1

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?

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Weights

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Number Daisy

Stage: 3 Challenge Level: Challenge Level:1

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?

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Two and Two

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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First Connect Three

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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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Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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More Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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First Connect Three for Two

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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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American Billions

Stage: 3 Challenge Level: Challenge Level:1

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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Ben's Game

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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Triangles to Tetrahedra

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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.

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Cuboids

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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Oranges and Lemons, Say the Bells of St Clement's

Stage: 3 Challenge Level: Challenge Level:1

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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Games Related to Nim

Stage: 1, 2, 3 and 4

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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Cayley

Stage: 3 Challenge Level: Challenge Level:1

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

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Plum Tree

Stage: 4 and 5 Challenge Level: Challenge Level:1

Label this plum tree graph to make it totally magic!

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Advent Calendar 2011 - Secondary

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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Pair Sums

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

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

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Tetrahedra Tester

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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M, M and M

Stage: 3 Challenge Level: Challenge Level:1

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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Building with Longer Rods

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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More Children and Plants

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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An Introduction to Magic Squares

Stage: 1, 2, 3 and 4

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

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Advent Sudoku

Stage: 3 Challenge Level: Challenge Level:1

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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More Plant Spaces

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Intersection Sudoku 1

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

A Sudoku with a twist.

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Addition Equation Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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A Long Time at the Till

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Difference Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the differences to find the solution to this Sudoku.

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The Great Weights Puzzle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Crossing the Town Square

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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Factors and Multiple Challenges

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Multiply the Addition Square

Stage: 3 Challenge Level: Challenge Level:1

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?

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Quadruple Clue Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.

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Colour Islands Sudoku

Stage: 3 Challenge Level: Challenge Level:1

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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Another Quadruple Clue Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.

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Pole Star Sudoku 2

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

This Sudoku, based on differences. Using the one clue number can you find the solution?

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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.

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

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

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LCM Sudoku II

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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Sociable Cards

Stage: 3 Challenge Level: Challenge Level:1

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?