Resources tagged with Working systematically similar to Divisibility Tests:
Other tags that relate to Divisibility Tests
Modulus arithmetic. Long problems. Index notation/Indices. Number theory. Digital roots. Divisibility. Mathematical reasoning & proof. Mathematical induction. Factors and multiples. Working systematically.There are 108 results
Latin Squares
Stage: 2, 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.
Product Sudoku 2
Stage: 3, 4 and 5 Challenge Level: 
Given the products of diagonally opposite cells - can you complete this Sudoku?
LCM Sudoku II
Stage: 3, 4 and 5 Challenge Level:
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Cayley
Stage: 3 Challenge Level:
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
All-variables Sudoku
Stage: 3, 4 and 5 Challenge Level:
The challenge is to find the values of the variables if you are to solve this Sudoku.
Consecutive Sums
Stage: 3 Challenge Level:
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?
Equation Sudoku
Stage: 3, 4 and 5 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
Product Sudoku
Stage: 3, 4 and 5 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
Quadruple Clue Sudoku
Stage: 3 and 4 Challenge Level:
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Where Can We Visit?
Stage: 3 Challenge Level:
Charlie and Lynne 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?
American Billions
Stage: 3 Challenge Level:
Find the ten-digit number in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3, the first four digits make a number divisible by 4...
Addition Equation Sudoku
Stage: 3, 4 and 5 Challenge Level:
You need to find the values of the stars before you can apply normal Sudoku rules.
LCM Sudoku
Stage: 4 and 5 Challenge Level:
Use the information about the lowest common multiples of the unknown numbers to help you solve this Sudoku.
Multiplication Equation Sudoku
Stage: 4 and 5 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.
Quadruple Clue Sudoku
Stage: 3 and 4 Challenge Level:
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Cuboids
Stage: 3 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?
A First Product Sudoku
Stage: 3 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
Wallpaper Sudoku
Stage: 3 and 4 Challenge Level:
A Sudoku that uses transformations as supporting clues.
Consecutive Numbers
Stage: 2 and 3 Challenge Level:
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Corresponding Sudokus
Stage: 3, 4 and 5
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
LOGO Challenge - Triangles-squares-stars
Stage: 3 and 4 Challenge Level:
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
The Great Weights Puzzle
Stage: 4 Challenge Level:
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Magic Caterpillars
Stage: 4 and 5 Challenge Level:
Put numbers 1 to n on the edges and vertices of a graph so that the sum of the numbers on a vertex and on all arcs joined to that vertex is the same for all vertices.
Weights
Stage: 3 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Quadruple Sudoku
Stage: 3 and 4 Challenge Level:
Four small numbers give the clue to the contents of the four surrounding cells.
Making Maths: Double-sided Magic Square
Stage: 2 and 3 Challenge Level:
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Twin Corresponding Sudokus II
Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Twin Corresponding Sudoku III
Stage: 3 and 4 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
Multiply the Addition Square
Stage: 3 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?
Sticky Numbers
Stage: 3 Challenge Level:
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Spot the Card
Stage: 4 Challenge Level:
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
Factors and Multiple Challenges
Stage: 3 Challenge Level:
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. . . .
Seasonal Twin Sudokus
Stage: 3 and 4 Challenge Level:
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Peaches Today, Peaches Tomorrow....
Stage: 3 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?
Ben's Game
Stage: 3 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.
An Introduction to Magic Squares
Stage: 1, 2 and 3
Find out about Magic Squares in this article written for students. Why are they magic?!
Twin Line-swapping Sudoku
Stage: 4 Challenge Level:
A pair of Sudoku puzzles that together lead to a complete solution.
Ones Only
Stage: 3 Challenge Level:
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
How Old Are the Children?
Stage: 3 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?"
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.
Number Daisy
Stage: 3 Challenge Level:
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 35?
Pole Star Sudoku
Stage: 4 and 5 Challenge Level:
A Sudoku based on clues that give the differences between adjacent cells.
Olympic Magic
Stage: 4 Challenge Level:
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Football Sum
Stage: 3 Challenge Level:
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Intersection Sums Sudoku
Stage: 2, 3 and 4 Challenge Level:
A Sudoku with clues given as sums of entries.
Route to Infinity
Stage: 3 Challenge Level:
Take some time to look at the route the arrows follow in this diagram. Through how many points does the route pass before it reaches the point (9,4)?
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