Resources tagged with: Trial and improvement

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Broad Topics > Thinking Mathematically > Trial and improvement

Augustus' Age

Age 7 to 11 Challenge Level:

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

3388

Age 11 to 14 Challenge 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.

Plenty of Pens

Age 7 to 11 Challenge 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?

Charitable Pennies

Age 7 to 14 Challenge Level:

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Going to the Cinema

Age 11 to 16

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

Fractions in a Box

Age 7 to 11 Challenge 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.

Arrange the Digits

Age 11 to 14 Challenge 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?

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.

Alphabet Soup

Age 11 to 14 Challenge Level:

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

Gift Stacks

Age 7 to 11 Challenge Level:

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

Sisters and Brothers

Age 7 to 11 Challenge 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?

Domino Square

Age 7 to 11 Challenge Level:

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Buckets of Thinking

Age 7 to 11 Challenge 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.

Cycling Squares

Age 7 to 11 Challenge Level:

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

In the Money

Age 7 to 11 Challenge Level:

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

Four Colours

Age 5 to 11 Challenge 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.

4 Dom

Age 5 to 16 Challenge Level:

Use these four dominoes to make a square that has the same number of dots on each side.

Make 100

Age 7 to 11 Challenge Level:

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

Pizza Cut

Age 7 to 11 Challenge 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).

A Mean Tetrahedron

Age 11 to 14 Challenge Level:

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

How Many Eggs?

Age 7 to 11 Challenge 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.

Magic Matrix

Age 7 to 11 Challenge Level:

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

Cat Food

Age 7 to 11 Challenge 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?

Fifteen Cards

Age 7 to 11 Challenge Level:

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

Dice Stairs

Age 7 to 11 Challenge Level:

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

Strike it Out for Two

Age 5 to 11 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Tom's Number

Age 7 to 11 Challenge Level:

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

Numbered Cars

Age 7 to 11 Challenge 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?

Sticky Dice

Age 7 to 11 Challenge 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?

Treasure Hunt

Age 7 to 14 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Got a Strategy for Last Biscuit?

Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

One Million to Seven

Age 7 to 11 Challenge 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?

Sliding Game

Age 7 to 11 Challenge Level:

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

One to Eight

Age 11 to 14 Challenge 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.

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?

Escape from the Castle

Age 7 to 11 Challenge 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?

Top-heavy Pyramids

Age 11 to 14 Challenge Level:

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Fitted

Age 7 to 11 Challenge 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?

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?

A Numbered Route

Age 7 to 11 Challenge 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?

Strike it Out

Age 5 to 11 Challenge Level:

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Paw Prints

Age 7 to 11 Challenge 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?

Path to the Stars

Age 7 to 11 Challenge Level:

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Sports Equipment

Age 7 to 11 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Four-digit Targets

Age 7 to 11 Challenge Level:

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

The Clockmaker's Birthday Cake

Age 7 to 11 Challenge Level:

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

Factor-multiple Chains

Age 7 to 11 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

Rocco's Race

Age 7 to 11 Short Challenge 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.

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?