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Resources tagged with Working systematically similar to Reasonable Algebra:

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

Plum Tree

Stage: 4 and 5 Challenge Level:

Label this plum tree graph to make it totally magic!

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.

Intersection Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Equation Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

Intersection Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Stage: 3, 4 and 5 Challenge Level:

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

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.

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.

Magic W

Stage: 4 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.

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.

Pole Star Sudoku

Stage: 4 and 5 Challenge Level:

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

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.

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?

Ratio Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Twin Corresponding Sudokus II

Stage: 3 and 4 Challenge Level:

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

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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. . . .

Games Related to Nim

Stage: 1, 2, 3 and 4

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.

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?

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.

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.

Product Sudoku

Stage: 3, 4 and 5 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

Ratio Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

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

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.

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?

Difference Sudoku

Stage: 3 and 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

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.

Cinema Problem

Stage: 3 and 4 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.

LOGO Challenge - Sequences and Pentagrams

Stage: 3, 4 and 5 Challenge Level:

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

Stage: 3 and 4 Challenge Level:

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

LCM Sudoku

Stage: 4 Challenge Level:

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

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.

Intersection Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

Instant Insanity

Stage: 3, 4 and 5 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.

One Out One Under

Stage: 4 Challenge 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?

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?

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

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?

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.

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

Olympic Magic

Stage: 4 Challenge 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?

Diagonal Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Bochap Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku combines all four arithmetic operations.

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

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.

Alphabetti Sudoku

Stage: 3 and 4 Challenge Level:

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

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.