# Resources tagged with: Working systematically

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Broad Topics > Mathematical Thinking > Working systematically ### Football Sum

##### Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME ##### Age 11 to 14 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? ### Special Numbers

##### Age 11 to 14 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? ##### Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E ### Two and Two

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 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"? ##### Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed? ### LCM Sudoku II

##### Age 11 to 18 Challenge Level:

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku. ### Ben's Game

##### Age 11 to 14 Challenge Level:

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. ##### Age 11 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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... ### Reach 100

##### Age 7 to 14 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. ### 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. ### 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. ### LCM Sudoku

##### Age 14 to 16 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it. ### All-variables Sudoku

##### Age 11 to 18 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers? ### Twin Line-swapping Sudoku

##### Age 14 to 16 Challenge Level:

A pair of Sudoku puzzles that together lead to a complete solution. ### Intersection Sudoku 1

##### Age 11 to 16 Challenge Level:

A Sudoku with a twist. ### Star Product Sudoku

##### Age 11 to 16 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. ##### Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be? ### 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? ##### Age 11 to 16 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. ### Corresponding Sudokus

##### Age 11 to 18

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

##### Age 11 to 16 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections. ### An Introduction to Magic Squares

##### Age 7 to 16 ### Twin Corresponding Sudoku

##### Age 11 to 18 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

A Sudoku that uses transformations as supporting clues. ### Difference Sudoku

##### Age 14 to 16 Challenge Level:

Use the differences to find the solution to this Sudoku. ### Seasonal Twin Sudokus

##### Age 11 to 16 Challenge Level:

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

##### Age 14 to 16 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. ### The Great Weights Puzzle

##### Age 14 to 16 Challenge Level:

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? ### Cinema Problem

##### Age 11 to 14 Challenge Level:

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. ### A First Product Sudoku

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 18

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. ##### Age 11 to 16 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. ### Colour Islands Sudoku

##### Age 11 to 14 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. ### 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. ### 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. ### 9 Weights

##### Age 11 to 14 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? ### Simultaneous Equations Sudoku

##### Age 11 to 16 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

Can you use your powers of logic and deduction to work out the missing information in these sporty situations? ### A Long Time at the Till

##### Age 14 to 18 Challenge Level:

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? ### Sticky Numbers

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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? ##### Age 11 to 14 Challenge Level:

You need to find the values of the stars before you can apply normal Sudoku rules. ### Intersection Sudoku 2

##### Age 11 to 16 Challenge Level:

A Sudoku with a twist. ### Twin Corresponding Sudoku III

##### Age 11 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Use the clues about the shaded areas to help solve this sudoku