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

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Cops and Robbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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Find the Difference

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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Root Hunter

Stage: 5 Challenge Level: Challenge Level:1

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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Factor-multiple Chains

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Sums of Pairs

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?”

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Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Archery

Stage: 3 Challenge Level: Challenge Level:1

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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Top Coach

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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Lost

Stage: 3 Challenge Level: Challenge Level:1

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

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

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

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Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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How Many Miles to Go?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

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The Brown Family

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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Eggs in Baskets

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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Cinema Problem

Stage: 3 and 4 Challenge Level: Challenge Level:1

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.

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Fitted

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Cycling Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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One Wasn't Square

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Fractions in a Box

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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What's it Worth?

Stage: 3 and 4 Challenge Level: Challenge Level:1

There are lots of different methods to find out what the shapes are worth - how many can you find?

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Twenty Divided Into Six

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Make 100

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Watch the Clock

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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One to Eight

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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How Old Am I?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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Grouping Goodies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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The Puzzling Sweet Shop

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Chain of Changes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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One Big Triangle

Stage: 1 Challenge Level: Challenge Level:1

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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Number Round Up

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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4 Dom

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Five Steps to 50

Stage: 1 Challenge Level: Challenge Level:1

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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Strike it Out for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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All Change

Stage: 1 Challenge Level: Challenge Level:1

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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Fifteen Cards

Stage: 2 Challenge Level: Challenge Level:1

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

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Escape from the Castle

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Jumping Squares

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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Sports Equipment

Stage: 2 Challenge Level: Challenge Level:1

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?

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Factor Track

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Introducing NRICH TWILGO

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

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

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Inky Cube

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Well Balanced

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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.

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Strike it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Coded Hundred Square

Stage: 2 Challenge Level: Challenge Level:1

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

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Two-digit Targets

Stage: 1 Challenge Level: Challenge Level:1

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

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Four-digit Targets

Stage: 2 Challenge Level: Challenge Level:1

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?

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Junior Frogs

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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In the Bag

Stage: 3 Challenge Level: Challenge Level:1

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?