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Resources tagged with Working systematically similar to And So on and So On:

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

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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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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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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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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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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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Product Doubles Sudoku

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

Each clue number in this sudoku is the product of the two numbers in adjacent 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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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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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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Constellation Sudoku

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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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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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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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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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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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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Football Sum

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

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

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Integrated Product Sudoku

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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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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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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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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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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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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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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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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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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Latin Squares

Stage: 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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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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LOGO Challenge - Sequences and Pentagrams

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

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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Quadruple Sudoku

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

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

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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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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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Magnetic Personality

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

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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Intersection Sudoku 1

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

A Sudoku with a twist.

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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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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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Cinema Problem

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

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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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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Integrated Sums Sudoku

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

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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Multiplication Equation Sudoku

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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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 Dynamics

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

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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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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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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I've Submitted a Solution - What Next?

Stage: 1, 2, 3, 4 and 5

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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Olympic Logic

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

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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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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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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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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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?