# Resources tagged with: Working systematically

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### There are 74 results

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

### 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.

### 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.

### 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.

### Purr-fection

##### Age 16 to 18 Challenge Level:

What is the smallest perfect square that ends with the four digits 9009?

### 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.

### 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.

### W Mates

##### Age 16 to 18 Challenge Level:

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

##### 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.

### Simultaneous Equations Sudoku

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

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

##### 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?

### Intersection Sudoku 2

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

A Sudoku with a twist.

### Plum Tree

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

Label this plum tree graph to make it totally magic!

### Diagonal Product Sudoku

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

##### 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.

### Function Pyramids

##### Age 16 to 18 Challenge Level:

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

### Warmsnug Double Glazing

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

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

### Interpolating Polynomials

##### Age 16 to 18 Challenge Level:

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

### Intersection Sudoku 1

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

A Sudoku with a twist.

### 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?

### Magnetic Personality

##### Age 7 to 16 Challenge Level:

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

### The Best Card Trick?

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

### Twin Line-swapping Sudoku

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

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

### 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?

### Bochap Sudoku

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

This Sudoku combines all four arithmetic operations.

### Integrated Sums Sudoku

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

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. . . .

### Twin Corresponding Sudokus II

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

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

### Magic Caterpillars

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

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

### Colour Islands Sudoku 2

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

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

### Twin Corresponding Sudoku III

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

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

### Rectangle Outline Sudoku

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

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

### Rainstorm Sudoku

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

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

### 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?

### Advent Calendar 2011 - Secondary

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

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

### Twin Chute-swapping Sudoku

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

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

### 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.

### Integrated Product Sudoku

##### Age 11 to 16 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.

### 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 Sudoku

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

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

### Exhaustion

##### Age 16 to 18 Challenge Level:

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

### Intersection Sums Sudoku

##### Age 7 to 16 Challenge Level:

A Sudoku with clues given as sums of entries.

### Instant Insanity

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Alphabetti Sudoku

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

This Sudoku requires you to do some working backwards before working forwards.

### Pole Star Sudoku

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

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

### 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.

### Constellation Sudoku

##### Age 14 to 18 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.

### Wallpaper Sudoku

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

A Sudoku that uses transformations as supporting clues.

### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18 Challenge Level:

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.

### Latin Lilies

##### Age 7 to 16 Challenge Level:

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

### Knights Moving

##### Age 16 to 18 Challenge Level:

Can you swap the black knights with the white knights in the minimum number of moves?