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Resources tagged with Working systematically similar to An Introduction to Irrational Numbers:

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

Stage: 3, 4 and 5 Challenge Level:

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

A Long Time at the Till

Stage: 4 and 5 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?

The Great Weights Puzzle

Stage: 4 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?

Integrated Sums Sudoku

Stage: 3 and 4 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. . . .

Pole Star Sudoku

Stage: 4 and 5 Challenge Level:

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

Stage: 3 and 4 Challenge Level:

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

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.

Bochap Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku combines all four arithmetic operations.

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.

Seasonal Twin Sudokus

Stage: 3 and 4 Challenge Level:

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

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

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

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.

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.

Stage: 3, 4 and 5 Challenge Level:

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

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.

Colour Islands Sudoku 2

Stage: 3, 4 and 5 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.

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

Twin Corresponding Sudokus II

Stage: 3 and 4 Challenge Level:

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

Twin Corresponding Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

Product Doubles Sudoku

Stage: 3 and 4 Challenge Level:

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

Difference Dynamics

Stage: 4 and 5 Challenge Level:

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?

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.

Twin Chute-swapping Sudoku

Stage: 4 and 5 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?

Rainstorm Sudoku

Stage: 4 Challenge Level:

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

Rectangle Outline Sudoku

Stage: 3 and 4 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.

Twin Corresponding Sudoku III

Stage: 3 and 4 Challenge Level:

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

Equation Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

Summing Consecutive Numbers

Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Introducing NRICH TWILGO

Stage: 1, 2, 3, 4 and 5 Challenge Level:

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Magic Caterpillars

Stage: 4 and 5 Challenge Level:

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

Ratio Sudoku 3

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

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

Olympic Logic

Stage: 3 and 4 Challenge Level:

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

Ratio Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

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.

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.

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?

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

Stage: 3 Challenge Level:

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?

LOGO Challenge - the Logic of LOGO

Stage: 3 and 4 Challenge Level:

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

LOGO Challenge - Following On

Stage: 3, 4 and 5 Challenge Level:

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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?

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.

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.

Multiplication Equation Sudoku

Stage: 4 and 5 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.

Ratio Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Intersection Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

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?

Cinema Problem

Stage: 3 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.

Magnetic Personality

Stage: 2, 3 and 4 Challenge Level:

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