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

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Sandwiches

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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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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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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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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Domino Square

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

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

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Sliding Game

Stage: 2 Challenge Level: Challenge Level:1

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

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Only Connect

Stage: 3 Challenge Level: Challenge Level:1

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?

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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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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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Tower Rescue

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

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

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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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Four Colours

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

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.

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3388

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

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.

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Got a Strategy for Last Biscuit?

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

Can you beat the computer in the challenging strategy game?

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Pair Sums

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Football Champs

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

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

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Gr8 Coach

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

Can you coach your rowing eight to win?

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One Million to Seven

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

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?

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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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Top-heavy Pyramids

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

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

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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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Difference

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

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

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

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?

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A Mean Tetrahedron

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

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?

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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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Arranging the Tables

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

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.

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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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Arrange the Digits

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

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?

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1, 2, 3, 4, 5

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

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?

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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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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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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?

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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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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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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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Dice Stairs

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

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

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Paw Prints

Stage: 2 Challenge Level: Challenge Level:1

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?

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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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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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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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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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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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Magic Triangle

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

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

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Augustus' Age

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

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?

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Plenty of Pens

Stage: 2 Challenge Level: Challenge Level:1

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?

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Three Cubed

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

Can you make a 3x3 cube with these shapes made from small cubes?

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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?