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Resources tagged with Working systematically similar to Powerful Factorial:

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

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Factors and Multiple Challenges

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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Ones Only

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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Cuboids

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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How Old Are the Children?

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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A First Product Sudoku

Stage: 3 Challenge Level: Challenge Level:1

Given the products of adjacent cells, can you complete this Sudoku?

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Multiply the Addition Square

Stage: 3 Challenge Level: Challenge Level:1

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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Product Sudoku

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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Special Numbers

Stage: 3 Challenge Level: Challenge Level:1

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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LCM Sudoku

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

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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Shopping Basket

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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Product Sudoku 2

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

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American Billions

Stage: 3 Challenge Level: Challenge Level:1

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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LCM Sudoku II

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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Where Can We Visit?

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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Multiplication Equation Sudoku

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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Ben's Game

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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Latin Squares

Stage: 3, 4 and 5

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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Peaches Today, Peaches Tomorrow....

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

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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Factor Lines

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Two and Two

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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More Magic Potting Sheds

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Number Daisy

Stage: 3 Challenge Level: Challenge Level:1

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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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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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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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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Integrated Product Sudoku

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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M, M and M

Stage: 3 Challenge Level: Challenge Level:1

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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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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Product Doubles Sudoku

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

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

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Rectangle Outline Sudoku

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

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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Seasonal Twin Sudokus

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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The Best Card Trick?

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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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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Rainstorm Sudoku

Stage: 4 Challenge Level: Challenge Level:1

Use the clues about the shaded areas to help solve this sudoku

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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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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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Magic Caterpillars

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

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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Weights

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Squares in Rectangles

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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Twin Line-swapping Sudoku

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

A pair of Sudoku puzzles that together lead to a complete solution.

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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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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".

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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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Colour Islands Sudoku 2

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

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

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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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Twin Corresponding Sudoku

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

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Twin Corresponding Sudokus II

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

Two sudokus in one. Challenge yourself to make the necessary connections.