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Resources tagged with Trial and improvement similar to Four Goodness Sake:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Trial and improvement

Got a Strategy for Last Biscuit?

Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

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?

Cops and Robbers

Age 7 to 16 Challenge Level:

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

Sending a Parcel

Age 11 to 14 Challenge Level:

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Gr8 Coach

Age 11 to 14 Challenge Level:

Can you coach your rowing eight to win?

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?

Long Multiplication

Age 11 to 14 Challenge Level:

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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?

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.

Lost

Age 11 to 14 Challenge Level:

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Sums of Pairs

Age 11 to 16 Challenge Level:

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

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?

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.

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.

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.

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?

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?

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?

Only Connect

Age 11 to 14 Challenge Level:

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Hallway Borders

Age 11 to 14 Challenge Level:

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

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.

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.

Factor Track

Age 7 to 14 Challenge Level:

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Area and Perimeter

Age 7 to 11 Challenge Level:

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

Tubular Path

Age 7 to 11 Challenge Level:

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

Inky Cube

Age 7 to 14 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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?

Fifteen Cards

Age 7 to 11 Challenge Level:

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

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?

Junior Frogs

Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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?

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?

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?

In the Bag

Age 11 to 14 Challenge Level:

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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.

How Many Miles to Go?

Age 11 to 14 Challenge 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?

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?

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 disc. Use the information to find out how many discs of each colour there are in the box.

Well Balanced

Age 5 to 18 Challenge Level:

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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.

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?

Magic Triangle

Age 7 to 11 Challenge Level:

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

Tower Rescue

Age 7 to 18 Challenge Level:

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

What Two ...?

Age 7 to 11 Short Challenge Level:

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

Special 24

Age 7 to 11 Challenge 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.

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.

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?

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).