Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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.

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.

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.

Colour in the Square

Age 7 to 16 Challenge 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?

Reach 100

Age 7 to 14 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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.

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?

Simultaneous Equations Sudoku

Age 11 to 16 Challenge Level:

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

Alphabetti Sudoku

Age 11 to 16 Challenge Level:

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

Cuboids

Age 11 to 14 Challenge Level:

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Football Sum

Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

Cayley

Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Two and Two

Age 11 to 16 Challenge Level:

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

Number Daisy

Age 11 to 14 Challenge Level:

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

More Magic Potting Sheds

Age 11 to 14 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?

Intersection Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

Intersection Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with a twist.

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?

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.

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.

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?

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?

Shady Symmetry

Age 11 to 14 Challenge Level:

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

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?

Tetrahedra Tester

Age 11 to 14 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?

The Moons of Vuvv

Age 7 to 11 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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.

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

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

Ratio Sudoku 3

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

Mystery Matrix

Age 7 to 11 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Counting on Letters

Age 11 to 14 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 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.

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

Age 11 to 14 Challenge Level:

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

Extra Challenges from Madras

Age 11 to 14 Challenge Level:

A few extra challenges set by some young NRICH members.

Magic Potting Sheds

Age 11 to 14 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?

How Long Does it Take?

Age 7 to 11 Challenge Level:

How long does it take to brush your teeth? Can you find the matching length of time?

Charitable Pennies

Age 7 to 14 Challenge Level:

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

One to Fifteen

Age 7 to 11 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Ratio Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

Build it Up

Age 7 to 11 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Button-up Some More

Age 7 to 11 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Latin Lilies

Age 7 to 16 Challenge Level:

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Inky Cube

Age 7 to 14 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Product Sudoku

Age 11 to 16 Challenge Level:

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