Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

One Out One Under

Age 14 to 16
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?

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?

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?

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.

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?

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.

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.

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.

Olympic Magic

Age 14 to 16
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?

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.

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?

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.

Advent Sudoku

Age 11 to 14
Challenge Level

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

Integrated Product Sudoku

Age 11 to 16
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.

Wallpaper Sudoku

Age 11 to 16
Challenge Level

A Sudoku that uses transformations as supporting clues.

Ratio Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

Ratio Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

Extra Challenges from Madras

Age 11 to 14
Challenge Level

A few extra challenges set by some young NRICH members.

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?

Intersection Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with a twist.

Tea Cups

Age 7 to 14
Challenge Level

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Integrated Sums Sudoku

Age 11 to 16
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. . . .

Bochap Sudoku

Age 11 to 16
Challenge Level

This Sudoku combines all four arithmetic operations.

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?

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?

Rainstorm Sudoku

Age 14 to 16
Challenge Level

Use the clues about the shaded areas to help solve this sudoku

Rectangle Outline Sudoku

Age 11 to 16
Challenge Level

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Twin Corresponding Sudoku III

Age 11 to 16
Challenge Level

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

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.

Isosceles Triangles

Age 11 to 14
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?

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.

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.

Pole Star Sudoku 2

Age 11 to 16
Challenge Level

This Sudoku, based on differences. Using the one clue number can you find the solution?

Making a Difference

Age 11 to 14
Challenge Level

How many different differences can you make?

More on Mazes

Age 7 to 14

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Twin Corresponding Sudokus II

Age 11 to 16
Challenge Level

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

Spot the Card

Age 14 to 16
Challenge Level

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Teddy Town

Age 5 to 14
Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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?

Simultaneous Equations Sudoku

Age 11 to 16
Challenge Level

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

Number Sandwiches

Age 7 to 14
Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?

Ones Only

Age 11 to 14
Challenge Level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Intersection Sums Sudoku

Age 7 to 16
Challenge Level

A Sudoku with clues given as sums of entries.

Intersection Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with a twist.

First Connect Three

Age 7 to 14
Challenge Level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Twinkle Twinkle

Age 7 to 14
Challenge Level

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Diagonal Sums Sudoku

Age 7 to 16
Challenge Level

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