Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Age 11 to 18Challenge Level

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

A Long Time at the Till

Age 14 to 18Challenge 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?

Exhaustion

Age 16 to 18Challenge Level

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

All-variables Sudoku

Age 11 to 18Challenge Level

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

Twin Corresponding Sudoku

Age 11 to 18Challenge Level

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

Interpolating Polynomials

Age 16 to 18Challenge 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.

Colour Islands Sudoku 2

Age 11 to 18Challenge 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.

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.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18Challenge 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.

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.

Difference Dynamics

Age 14 to 18Challenge 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?

Age 11 to 16Challenge 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.

Magic W

Age 14 to 16Challenge 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.

Twin Chute-swapping Sudoku

Age 14 to 18Challenge 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?

The Great Weights Puzzle

Age 14 to 16Challenge 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?

Simultaneous Equations Sudoku

Age 11 to 16Challenge Level

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

Magic Caterpillars

Age 14 to 18Challenge Level

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

Ratio Sudoku 3

Age 11 to 16Challenge Level

A Sudoku with clues as ratios or fractions.

An Introduction to Magic Squares

Age 11 to 16Challenge 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.

Ratio Sudoku 2

Age 11 to 16Challenge Level

A Sudoku with clues as ratios.

Intersection Sudoku 1

Age 11 to 16Challenge Level

A Sudoku with a twist.

Star Product Sudoku

Age 11 to 16Challenge 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.

Plum Tree

Age 14 to 18Challenge Level

Label this plum tree graph to make it totally magic!

LCM Sudoku II

Age 11 to 18Challenge Level

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

Two and Two

Age 11 to 16Challenge Level

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

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.

Smith and Jones

Age 14 to 16Challenge Level

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

Olympic Magic

Age 14 to 16Challenge Level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

Integrated Product Sudoku

Age 11 to 16Challenge 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.

Diagonal Product Sudoku

Age 11 to 16Challenge Level

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

Ratio Sudoku 1

Age 11 to 16Challenge Level

A Sudoku with clues as ratios.

Knights Moving

Age 16 to 18Challenge Level

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

W Mates

Age 16 to 18Challenge 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.

One Out One Under

Age 14 to 16Challenge Level

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

Intersection Sudoku 2

Age 11 to 16Challenge Level

A Sudoku with a twist.

LOGO Challenge - Triangles-squares-stars

Age 11 to 16Challenge Level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

I've Submitted a Solution - What Next?

Age 5 to 18

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

Pole Star Sudoku

Age 14 to 18Challenge Level

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

Colour in the Square

Age 7 to 16Challenge 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?

Constellation Sudoku

Age 14 to 18Challenge 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.

Alphabetti Sudoku

Age 11 to 16Challenge Level

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

Function Pyramids

Age 16 to 18Challenge 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?

Bochap Sudoku

Age 11 to 16Challenge Level

This Sudoku combines all four arithmetic operations.

Olympic Logic

Age 11 to 16Challenge Level

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

Twin Corresponding Sudoku III

Age 11 to 16Challenge Level

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

Binomial Coefficients

Age 14 to 18

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

Intersection Sums Sudoku

Age 7 to 16Challenge Level

A Sudoku with clues given as sums of entries.

Purr-fection

Age 16 to 18Challenge Level

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