Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Multiples Sudoku

Age 11 to 14
Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

American Billions

Age 11 to 14
Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Product Sudoku

Age 11 to 16
Challenge Level

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

Code Breaker

Age 7 to 11
Challenge Level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

A First Product Sudoku

Age 7 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

How Old Are the Children?

Age 11 to 14
Challenge Level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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?

ABC

Age 7 to 11
Challenge Level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Today's Date - 01/06/2009

Age 5 to 11
Challenge Level

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

Two Egg Timers

Age 7 to 11
Challenge Level

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?

Adding Plus

Age 7 to 11
Challenge Level

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?

Prison Cells

Age 7 to 11
Challenge Level

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?

Spell by Numbers

Age 7 to 11
Challenge Level

Can you substitute numbers for the letters in these sums?

Twenty Divided Into Six

Age 7 to 11
Challenge Level

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Seven Square Numbers

Age 7 to 11
Challenge Level

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.

Two Primes Make One Square

Age 7 to 11
Challenge Level

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

Star Product Sudoku

Age 11 to 16
Challenge Level

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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?

Pouring the Punch Drink

Age 7 to 11
Challenge Level

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.

The Pied Piper of Hamelin

Age 7 to 11
Challenge Level

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!

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

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

Factor Lines

Age 7 to 14
Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A Mixed-up Clock

Age 7 to 11
Challenge Level

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

How Much Did it Cost?

Age 7 to 11
Challenge Level

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Arranging the Tables

Age 7 to 11
Challenge Level

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.

Cinema Problem

Age 11 to 14
Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Zargon Glasses

Age 7 to 11
Challenge Level

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?

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?

The Puzzling Sweet Shop

Age 5 to 11
Challenge Level

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Ben's Game

Age 11 to 16
Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

A-magical Number Maze

Age 7 to 11
Challenge Level

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!

Dart Target

Age 7 to 11
Challenge Level

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.

Being Resourceful - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that require careful consideration.

Gabriel's Problem

Age 11 to 14
Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Oh! Harry!

Age 7 to 11
Challenge Level

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Pair Sums

Age 11 to 14
Challenge Level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Six Is the Sum

Age 7 to 11
Challenge Level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

On Target

Age 7 to 11
Challenge Level

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

Prompt Cards

Age 7 to 11
Challenge Level

These two group activities use mathematical reasoning - one is numerical, one geometric.

X Is 5 Squares

Age 7 to 11
Challenge Level

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

Dice and Spinner Numbers

Age 7 to 11
Challenge Level

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?

The Dice Train

Age 7 to 11
Challenge Level

This dice train has been made using specific rules. How many different trains can you make?

How Old?

Age 7 to 11
Challenge Level

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

Hubble, Bubble

Age 7 to 11
Challenge Level

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?

A Square of Numbers

Age 7 to 11
Challenge Level

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

Number Detective

Age 5 to 11
Challenge Level

Follow the clues to find the mystery number.

Extra Challenges from Madras

Age 11 to 14
Challenge Level

A few extra challenges set by some young NRICH members.

Ladybird Box

Age 5 to 11
Challenge Level

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Build it up More

Age 7 to 11
Challenge Level

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