# Resources tagged with: Trial and improvement

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### There are 85 results

Broad Topics > Thinking Mathematically > Trial and improvement

### Factor-multiple Chains

##### Age 7 to 11Challenge 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?

### Strike it Out for Two

##### Age 5 to 11Challenge Level

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

### Strike it Out

##### Age 5 to 11Challenge Level

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

### Daisy

##### Age 7 to 11Challenge Level

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

### Make 100

##### Age 7 to 11Challenge Level

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

### 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?

### Domino Square

##### Age 7 to 11Challenge Level

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

### Sliding Game

##### Age 7 to 11Challenge Level

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

### 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.

### Cycling Squares

##### Age 7 to 11Challenge 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 11Challenge 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-digit Targets

##### Age 7 to 11Challenge Level

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

### Coded Hundred Square

##### Age 7 to 11Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

### 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'.

### In the Bag

##### Age 11 to 14Challenge 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?

### Magic Potting Sheds

##### Age 11 to 14Challenge 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?

### Junior Frogs

##### Age 5 to 11Challenge Level

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

### Number Sandwiches

##### Age 7 to 14Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

### 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).

### What Two ...?

##### Age 7 to 11 ShortChallenge Level

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

### Fence It

##### Age 11 to 14Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

### 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.

### Charitable Pennies

##### Age 7 to 14Challenge Level

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

### 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?

### 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?

### Going to the Cinema

##### Age 11 to 16

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

### Sums of Pairs

##### Age 11 to 16Challenge 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?”

### 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?

### Sending a Parcel

##### Age 11 to 14Challenge Level

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

### Treasure Hunt

##### Age 7 to 14Challenge Level

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

### 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?

### 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?

### 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.

### Escape from the Castle

##### Age 7 to 14Challenge 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?

### 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.

### 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?

### 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.

### Inky Cube

##### Age 7 to 14Challenge 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?

### 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.

### 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?

### 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 Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

### Path to the Stars

##### Age 7 to 11Challenge 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?

### Fifteen Cards

##### Age 7 to 11Challenge Level

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

### 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?

### Alphabet Soup

##### Age 11 to 14Challenge 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.

### 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.

### 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 Mean Tetrahedron

##### Age 11 to 14Challenge 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 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.

### 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.