Resources tagged with Working systematically similar to Digat:
Other tags that relate to Digat
Multiplication & division. Prime factors. Properties of numbers. Factors and multiples. Common factors. Mathematical reasoning & proof. Modular arithmetic. Square numbers. Working systematically. Divisibility.There are 129 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically
Multiply the Addition Square
Age 11 to 14 Challenge Level:
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?
A First Product Sudoku
Age 11 to 14 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
Latin Squares
Age 11 to 18
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.
Star Product Sudoku
Age 11 to 16 Challenge Level:
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.
LCM Sudoku
Age 14 to 16 Challenge Level:
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Ben's Game
Age 11 to 14 Challenge Level:
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.
Factor Lines
Age 7 to 14 Challenge Level:
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Diagonal Product Sudoku
Age 11 to 16 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
How Old Are the Children?
Age 11 to 14 Challenge Level:
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?"
More Magic Potting Sheds
Age 11 to 14 Challenge Level:
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?
Peaches Today, Peaches Tomorrow...
Age 11 to 14 Challenge Level:
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?
LCM Sudoku II
Age 11 to 18 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
American Billions
Age 11 to 14 Challenge Level:
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...
Product Sudoku
Age 11 to 14 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Smith and Jones
Age 14 to 16 Challenge Level:
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
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?
Ones Only
Age 11 to 14 Challenge Level:
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
Cuboids
Age 11 to 14 Challenge Level:
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?
The Best Card Trick?
Age 11 to 16 Challenge Level:
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?
Shopping Basket
Age 11 to 16 Challenge Level:
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
9 Weights
Age 11 to 14 Challenge Level:
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?
Twin Chute-swapping Sudoku
Age 14 to 18 Challenge Level:
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
Sticky Numbers
Age 11 to 14 Challenge Level:
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
A Long Time at the Till
Age 14 to 18 Challenge Level:
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Summing Consecutive Numbers
Age 11 to 14 Challenge Level:
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Integrated Product Sudoku
Age 11 to 16 Challenge Level:
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.
Special Numbers
Age 11 to 14 Challenge Level:
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?
The Naked Pair in Sudoku
Age 7 to 16
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Difference Dynamics
Age 14 to 18 Challenge Level:
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Rainstorm Sudoku
Age 14 to 16 Challenge Level:
Use the clues about the shaded areas to help solve this sudoku
Multiples Sudoku
Age 11 to 14 Challenge Level:
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Difference Sudoku
Age 14 to 16 Challenge Level:
Use the differences to find the solution to this Sudoku.
Magnetic Personality
Age 7 to 16 Challenge Level:
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Twin Line-swapping Sudoku
Age 14 to 16 Challenge Level:
A pair of Sudoku puzzles that together lead to a complete solution.
LOGO Challenge - the Logic of LOGO
Age 11 to 16 Challenge Level:
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Advent Sudoku
Age 11 to 14 Challenge Level:
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Seasonal Twin Sudokus
Age 11 to 16 Challenge Level:
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Addition Equation Sudoku
Age 11 to 14 Challenge Level:
You need to find the values of the stars before you can apply normal Sudoku rules.
LOGO Challenge - Sequences and Pentagrams
Age 11 to 18 Challenge Level:
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Weights
Age 11 to 14 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Twin Corresponding Sudokus II
Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Twin Corresponding Sudoku III
Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Colour Islands Sudoku 2
Age 11 to 18 Challenge Level:
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.
Making Maths: Double-sided Magic Square
Age 7 to 14 Challenge Level:
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Rectangle Outline Sudoku
Age 11 to 16 Challenge Level:
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Where Can We Visit?
Age 11 to 14 Challenge Level:
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?
Olympic Logic
Age 11 to 16 Challenge Level:
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
I've Submitted a Solution - What Next?
Age 5 to 18
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
NRICH is part of the family of activities in the Millennium Mathematics Project.