Resources tagged with: Trial and improvement

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Broad Topics > Thinking Mathematically > Trial and improvement

Let's Face It

Age 7 to 11Challenge Level

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Numbered Cars

Age 7 to 11Challenge Level

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Oranges and Lemons

Age 7 to 11Challenge Level

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

One Million to Seven

Age 7 to 11Challenge Level

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Buckets of Thinking

Age 7 to 11Challenge Level

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Magic Circles

Age 7 to 11Challenge Level

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Rocco's Race

Age 7 to 11 ShortChallenge Level

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Sisters and Brothers

Age 7 to 11Challenge Level

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Zios and Zepts

Age 7 to 11Challenge Level

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Age 7 to 11Challenge Level

Use the information to work out how many gifts there are in each pile.

Number Juggle

Age 7 to 11Challenge Level

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Magic Triangle

Age 7 to 11Challenge Level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

One Wasn't Square

Age 7 to 11Challenge Level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

How Many Eggs?

Age 7 to 11Challenge Level

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Prison Cells

Age 7 to 11Challenge 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?

A Numbered Route

Age 7 to 11Challenge Level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Arranging the Tables

Age 7 to 11Challenge 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.

The Clockmaker's Birthday Cake

Age 7 to 11Challenge Level

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Rabbits in the Pen

Age 7 to 11Challenge 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 11Challenge 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?

Escape from the Castle

Age 7 to 11Challenge Level

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Sticky Dice

Age 7 to 11Challenge Level

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Clever Santa

Age 7 to 11Challenge Level

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Fractions in a Box

Age 7 to 11Challenge Level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

1, 2, 3, 4, 5

Age 7 to 11Challenge Level

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Cat Food

Age 7 to 11Challenge Level

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Magic Matrix

Age 7 to 11Challenge Level

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

Twenty Divided Into Six

Age 7 to 11Challenge 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?

Special 24

Age 7 to 11Challenge Level

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Arrange the Digits

Age 11 to 14Challenge Level

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Pizza Cut

Age 7 to 11Challenge Level

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

Fitted

Age 7 to 11Challenge Level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Cinema Problem

Age 11 to 14Challenge 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.

Dice Stairs

Age 7 to 11Challenge Level

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

Difference

Age 7 to 11Challenge Level

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

What Two ...?

Age 7 to 11 ShortChallenge Level

56 406 is the product of two consecutive numbers. What are these two numbers?

Paw Prints

Age 7 to 11Challenge Level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Plenty of Pens

Age 7 to 11Challenge Level

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Fifteen Cards

Age 7 to 11Challenge Level

Can you use the information to find out which cards I have used?

Going to the Cinema

Age 11 to 16

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

Make 100

Age 7 to 11Challenge Level

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Tom's Number

Age 7 to 11Challenge Level

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Area and Perimeter

Age 7 to 11Challenge Level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Pair Sums

Age 11 to 14Challenge Level

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

A Shapely Network

Age 7 to 11Challenge Level

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

3388

Age 11 to 14Challenge Level

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Highest and Lowest

Age 7 to 11Challenge Level

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Four Colours

Age 5 to 11Challenge Level

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.

How Many Miles to Go?

Age 11 to 14Challenge Level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

One to Eight

Age 11 to 14Challenge Level

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.