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Resources tagged with Working systematically similar to Weekly Problem 24 - 2011:

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

Stage: 3 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares?

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?

Tetrahedra Tester

Stage: 3 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Triangles to Tetrahedra

Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Squares in Rectangles

Stage: 3 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?

More Magic Potting Sheds

Stage: 3 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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.

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Maths Trails

Stage: 2 and 3

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.

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?

Where Can We Visit?

Stage: 3 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?

Twin Corresponding Sudoku III

Stage: 3 and 4 Challenge Level:

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

9 Weights

Stage: 3 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?

Building with Longer Rods

Stage: 2 and 3 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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.

Magic Potting Sheds

Stage: 3 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

First Connect Three

Stage: 2 and 3 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Intersection Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

Ratio Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

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?

Ratio Sudoku 2

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

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?

Intersection Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with a twist.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

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

Ratio Sudoku 3

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

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.

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.

Fault-free Rectangles

Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

Consecutive Negative Numbers

Stage: 3 Challenge Level:

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

Twin Corresponding Sudokus II

Stage: 3 and 4 Challenge Level:

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

Intersection Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

Hexpentas

Stage: 1 and 2 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Stage: 3 Challenge Level:

A few extra challenges set by some young NRICH members.

Difference

Stage: 2 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

M, M and M

Stage: 3 Challenge Level:

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

How Long Does it Take?

Stage: 2 Challenge Level:

In this matching game, you have to decide how long different events take.

Bochap Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku combines all four arithmetic operations.

Oranges and Lemons, Say the Bells of St Clement's

Stage: 3 Challenge Level:

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Combining Cuisenaire

Stage: 2 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

LOGO Challenge - Triangles-squares-stars

Stage: 3 and 4 Challenge 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.

Colour Islands Sudoku

Stage: 3 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.

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.

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.

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?