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Resources tagged with Working systematically similar to Going First:

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

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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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Pole Star Sudoku

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

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

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One Out One Under

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

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?

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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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Corresponding Sudokus

Stage: 3, 4 and 5

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

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Wallpaper Sudoku

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

A Sudoku that uses transformations as supporting clues.

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Twin Corresponding Sudoku III

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

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

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Twin Corresponding Sudokus II

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

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

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Noughts and Crosses

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

Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.

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Seasonal Twin Sudokus

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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Olympic Magic

Stage: 4 Challenge Level: Challenge Level:1

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?

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Ratio Sudoku 1

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

A Sudoku with clues as ratios.

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Twin Corresponding Sudoku

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

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

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Intersection Sums Sudoku

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

A Sudoku with clues given as sums of entries.

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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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Fence It

Stage: 3 Challenge Level: Challenge Level:1

A plot of land needs fencing to house some hens. If you have only 40 metres of fencing available, determine the value of x which will provide the hens with the maximum area.

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An Introduction to Magic Squares

Stage: 1, 2 and 3

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

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

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

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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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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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Ratio Sudoku 2

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

A Sudoku with clues as ratios.

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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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Consecutive Numbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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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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Magic W

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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You Owe Me Five Farthings, Say the Bells of St Martin's

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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Number Pyramids

Stage: 3 Challenge Level: Challenge Level:1

Using the same starter numbers 2, 1, 4 and 6 can you get a larger total at the top of the pyramid? What is the largest total you can get?

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Intersection Sudoku 2

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

A Sudoku with a twist.

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Cinema Problem

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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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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Magic Potting Sheds

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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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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When Will You Pay Me? Say the Bells of Old Bailey

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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Where Can We Visit?

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

Charlie and Lynne 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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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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Diagonal Sums Sudoku

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

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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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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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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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 35?

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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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Twin Line-swapping Sudoku

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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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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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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Plum Tree

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

Label a graph with the numbers 1 to n, one on each vertex, one on each arc. A Totally Magic graph is both Edge Magic and Vertex Magic.

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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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Latin Squares

Stage: 2, 3, 4 and 5

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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Magic Caterpillars

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

Put numbers 1 to n on the edges and vertices of a graph so that the sum of the numbers on a vertex and on all arcs joined to that vertex is the same for all vertices.

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The Best Card Trick Ever!

Stage: 4

You will need an assistant, a witness and an ordinary deck of cards.

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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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Peaches Today, Peaches Tomorrow....

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

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?