Resources tagged with: Trial and improvement

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Broad Topics > Thinking Mathematically > Trial and improvement

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?

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?

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.

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?

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.

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.

Got a Strategy for Last Biscuit?

Age 11 to 16
Challenge Level

Can you beat the computer in the challenging strategy game?

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?

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?

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).

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?

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?

Difference

Age 7 to 11
Challenge Level

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

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?

Charitable Pennies

Age 7 to 14
Challenge Level

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

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?

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?

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?

Magic Circles

Age 7 to 11
Challenge 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?

What Two ...?

Age 7 to 11 Short
Challenge Level

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

Fifteen Cards

Age 7 to 11
Challenge Level

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

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'.

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.

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?

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?

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?

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.

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?

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?

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?

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?”

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.

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?

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.

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.

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?

Going to the Cinema

Age 11 to 16

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

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?

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?

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.

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?

1, 2, 3, 4, 5

Age 7 to 11
Challenge 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?

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.

Let's Face It

Age 7 to 11
Challenge 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.

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.

Zios and Zepts

Age 7 to 11
Challenge 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?

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.

A Shapely Network

Age 7 to 11
Challenge 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.