Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Home Time

Age 7 to 11
Challenge Level

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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?

Watch the Clock

Age 7 to 11
Challenge Level

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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?

Intersection Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with a twist.

Intersection Sums Sudoku

Age 7 to 16
Challenge Level

A Sudoku with clues given as sums of entries.

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?

First Connect Three

Age 7 to 11
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?

A Child Is Full of ...

Age 7 to 11 Short
Challenge Level

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Twin Corresponding Sudokus II

Age 11 to 16
Challenge Level

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

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.

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.

Twin Corresponding Sudoku III

Age 11 to 16
Challenge Level

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

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 Product Sudoku

Age 11 to 16
Challenge Level

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

Counters

Age 7 to 11
Challenge Level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Ratio Sudoku 3

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios or fractions.

Shunting Puzzle

Age 7 to 11
Challenge Level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Single Track

Age 7 to 11
Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

How Many Times?

Age 7 to 11
Challenge Level

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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.

Waiting for Blast Off

Age 7 to 11
Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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.

Jigsaw Pieces

Age 7 to 11
Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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?

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 ...?

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.

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?

Putting Two and Two Together

Age 7 to 11
Challenge Level

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Fence It

Age 11 to 14
Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Latin Lilies

Age 7 to 14
Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

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.

Open Boxes

Age 7 to 11
Challenge Level

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

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.

Ratio Sudoku 2

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

Display Boards

Age 7 to 11
Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Intersection Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with a twist.

First Connect Three for Two

Age 7 to 11
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.

Daisy

Age 7 to 11
Challenge Level

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

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?

Quadrilaterals

Age 7 to 11
Challenge Level

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Fake Gold

Age 7 to 11
Challenge Level

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Coded Hundred Square

Age 7 to 11
Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

Rabbits in the Pen

Age 7 to 11
Challenge Level

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Arrangements

Age 7 to 11
Challenge Level

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?