Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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.

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.

Another Quadruple Clue Sudoku

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.

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?

Addition Equation Sudoku

Age 11 to 14
Challenge Level

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

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.

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.

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.

Simultaneous Equations Sudoku

Age 11 to 16
Challenge Level

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

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.

Intersection Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with a twist.

Pole Star Sudoku

Age 14 to 18
Challenge Level

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

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.

Read This Page

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

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.

Neighbourly Addition

Age 7 to 14
Challenge Level

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

Quadruple Clue 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.

Consecutive Negative Numbers

Age 11 to 14
Challenge Level

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

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.

Intersection Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with a twist.

Quadruple Sudoku

Age 11 to 16
Challenge Level

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

Twin Line-swapping Sudoku

Age 14 to 16
Challenge Level

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

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?

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.

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.

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?

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.

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.

Coins

Age 11 to 14
Challenge Level

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

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.

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.

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?

Gabriel's Problem

Age 11 to 14
Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Squares in Rectangles

Age 11 to 14
Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

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?

Charitable Pennies

Age 7 to 14
Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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.

Difference Dynamics

Age 14 to 18
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?

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?

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?

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?

Multiply the Addition Square

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?

How Old Are the Children?

Age 11 to 14
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?"

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?

Smith and Jones

Age 14 to 16
Challenge 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!

LOGO Challenge - Sequences and Pentagrams

Age 11 to 18
Challenge Level

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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?

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?

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...