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#### Resources tagged with Working systematically similar to Reverse Subtraction:

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

### 9 Weights

##### Stage: 3 Challenge Level:

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?

### Weights

##### Stage: 3 Challenge Level:

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

### Addition Equation Sudoku

##### Stage: 3 Challenge Level:

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

### Football Sum

##### Stage: 3 Challenge Level:

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

### Consecutive Numbers

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

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

### 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.

### More Magic Potting Sheds

##### Stage: 3 Challenge Level:

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?

### Cayley

##### Stage: 3 Challenge Level:

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

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

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

### Pair Sums

##### Stage: 3 Challenge Level:

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

### Sticky Numbers

##### Stage: 3 Challenge Level:

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

### Multiply the Addition Square

##### Stage: 3 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?

### Multiples Sudoku

##### Stage: 3 Challenge Level:

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

##### Stage: 3 Challenge Level:

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

### Special Numbers

##### Stage: 3 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?

##### Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

### Reach 100

##### Stage: 2 and 3 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.

### First Connect Three for Two

##### Stage: 2 and 3 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.

### Constellation Sudoku

##### Stage: 4 and 5 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.

### Making Maths: Double-sided Magic Square

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

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

### Magic Potting Sheds

##### Stage: 3 Challenge Level:

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?

### Integrated Product Sudoku

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

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.

### Colour Islands Sudoku

##### Stage: 3 Challenge Level:

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

### Intersection Sudoku 1

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

A Sudoku with a twist.

### 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?!

### Quadruple Clue Sudoku

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

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.

### Intersection Sudoku 2

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

A Sudoku with a twist.

### A First Product Sudoku

##### Stage: 3 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

### LCM Sudoku II

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

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

### Another Quadruple Clue Sudoku

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

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.

### Factor Lines

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

### Pole Star Sudoku 2

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

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

### Magic W

##### Stage: 4 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.

### Ones Only

##### Stage: 3 Challenge Level:

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

### Tetrahedra Tester

##### Stage: 3 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?

### How Old Are the Children?

##### Stage: 3 Challenge Level:

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

### Medal Muddle

##### Stage: 3 Challenge Level:

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

### Simultaneous Equations Sudoku

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

Solve the equations to identify the clue numbers in this Sudoku problem.

### Two and Two

##### Stage: 3 Challenge Level:

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

### Plum Tree

##### Stage: 4 and 5 Challenge Level:

Label this plum tree graph to make it totally magic!

### All-variables Sudoku

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

The challenge is to find the values of the variables if you are to solve this Sudoku.

### First Connect Three

##### Stage: 2 and 3 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?

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### Bochap Sudoku

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

This Sudoku combines all four arithmetic operations.

### Coins

##### Stage: 3 Challenge Level:

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

### Star Product Sudoku

##### Stage: 3 and 4 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.

### The Naked Pair in Sudoku

##### Stage: 2, 3 and 4

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

### Crossing the Bridge

##### Stage: 3 Challenge Level:

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

### 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.

### Peaches Today, Peaches Tomorrow....

##### Stage: 3 Challenge Level:

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?