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Resources tagged with Working systematically similar to Magic Constants:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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A-magical Number Maze

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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Rabbits in the Pen

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Adding Plus

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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Zargon Glasses

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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Pouring the Punch Drink

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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The Pied Piper of Hamelin

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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On Target

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have 5 darts and your target score is 44. How many different ways could you score 44?

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How Old?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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Hubble, Bubble

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Dart Target

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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Sums and Differences 2

Stage: 2 Challenge Level: Challenge Level:1

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Build it up More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This task follows on from Build it Up and takes the ideas into three dimensions!

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Build it Up

Stage: 2 Challenge Level: Challenge Level:1

Can you find all the ways to get 15 at the top of this triangle of numbers?

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Sums and Differences 1

Stage: 2 Challenge Level: Challenge Level:1

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Dice Stairs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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Two Egg Timers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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X Is 5 Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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Arranging the Tables

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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Room Doubling

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the different ways you could split up these rooms so that you have double the number.

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Building with Rods

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In how many ways can you stack these rods, following the rules?

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Halloween Investigation

Stage: 2 Challenge Level: Challenge Level:1

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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Sealed Solution

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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It Figures

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Calcunos

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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Train Carriages

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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Mystery Matrix

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Bean Bags for Bernard's Bag

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Two Primes Make One Square

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make square numbers by adding two prime numbers together?

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Make Pairs

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

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

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Page Numbers

Stage: 2 Short Challenge Level: Challenge Level:1

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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A Right Charlie

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you use this information to work out Charlie's house number?

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Two Dots

Stage: 2 Challenge Level: Challenge Level:1

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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Painting Possibilities

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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Seven Square Numbers

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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Route Product

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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Four Colours

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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Buying a Balloon

Stage: 2 Challenge Level: Challenge Level:1

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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Rolling That Cube

Stage: 1 and 2 Challenge Level: Challenge Level:1

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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Being Thoughtful - Primary Number

Stage: 1 and 2 Challenge Level: Challenge Level:1

Number problems at primary level that require careful consideration.

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3 Rings

Stage: 2 Challenge Level: Challenge Level:1

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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Dice and Spinner Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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Open Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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Centred Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.