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Resources tagged with Working systematically similar to Weekly Problem 18 - 2013:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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Tea Cups

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Crossing the Bridge

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

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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Pole Star Sudoku 2

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

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Team Scream

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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Extra Challenges from Madras

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

A few extra challenges set by some young NRICH members.

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Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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Neighbours

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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Masterclass Ideas: Working Systematically

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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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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Teddy Town

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Elf Suits

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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Olympic Logic

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

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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The Naked Pair in Sudoku

Stage: 2, 3 and 4

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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Sitting Round the Party Tables

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Instant Insanity

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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9 Weights

Stage: 3 Challenge Level: Challenge Level:1

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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Bean Bags for Bernard's Bag

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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Cayley

Stage: 3 Challenge Level: Challenge Level:1

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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1 to 8

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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Difference Sudoku

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

Use the differences to find the solution to this Sudoku.

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Quadruple Sudoku

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

Four small numbers give the clue to the contents of the four surrounding cells.

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Page Numbers

Stage: 2 Short Challenge Level: Challenge Level:1

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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Twinkle Twinkle

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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Shapes in a Grid

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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Diagonal Sums Sudoku

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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Football Sum

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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Colour Islands Sudoku

Stage: 3 Challenge Level: Challenge Level:1

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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Home City

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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Order the Changes

Stage: 2 Challenge Level: Challenge Level:1

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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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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First Connect Three

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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Coins

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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Plate Spotting

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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Ladybird Box

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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Through the Window

Stage: 2 Challenge Level: Challenge Level:1

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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Three by Three

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

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Penta Place

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

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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Shape Times Shape

Stage: 2 Challenge Level: Challenge Level:1

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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Roll These Dice

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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Calendar Cubes

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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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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The Third Dimension

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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Three Way Mix Up

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

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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Creating Cubes

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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Number Detective

Stage: 2 Challenge Level: Challenge Level:1

Follow the clues to find the mystery number.

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Whose Face?

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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Counting Cards

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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Family Tree

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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Advent Sudoku

Stage: 3 Challenge Level: Challenge Level:1

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".