Other tags that relate to Surds
Indices. Generalising. Powers & roots. Simultaneous equations. Diophantine equations. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Multiplication & division. Other equations. Working systematically.There are 133 results
Broad Topics > Thinking Mathematically > Working systematically
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?
Another Quadruple Clue Sudoku
Age 11 to 16 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.
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?
Simultaneous Equations Sudoku
Age 11 to 16 Challenge Level:
Solve the equations to identify the clue numbers in this Sudoku problem.
Cayley
Age 11 to 14 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"?
Two and Two
Age 11 to 16 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Colour Islands Sudoku
Age 11 to 14 Challenge Level:
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Football Sum
Age 11 to 14 Challenge Level:
Find the values of the nine letters in the sum: FOOT + BALL = GAME
All-variables Sudoku
Age 11 to 18 Challenge Level:
The challenge is to find the values of the variables if you are to solve this Sudoku.
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.
Add to 200
Age 11 to 14 Challenge Level:
By selecting digits for an addition grid, what targets can you make?
Gabriel's Problem
Age 11 to 14 Challenge Level:
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Charitable Pennies
Age 7 to 14 Challenge Level:
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Read This Page
Age 11 to 14 Challenge Level:
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Quadruple Clue Sudoku
Age 11 to 16 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.
Consecutive Negative Numbers
Age 11 to 14 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Twin Corresponding Sudokus II
Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
Diagonal Product Sudoku
Age 11 to 16 Challenge Level:
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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?
Product Sudoku
Age 11 to 16 Challenge Level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
Quadruple Sudoku
Age 11 to 16 Challenge Level:
Four small numbers give the clue to the contents of the four surrounding cells.
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.
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!
Twin Line-swapping Sudoku
Age 14 to 16 Challenge Level:
A pair of Sudoku puzzles that together lead to a complete solution.
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.
A First Product Sudoku
Age 11 to 14 Challenge Level:
Given the products of adjacent cells, can you complete this Sudoku?
Wallpaper Sudoku
Age 11 to 16 Challenge Level:
A Sudoku that uses transformations as supporting clues.
Peaches Today, Peaches Tomorrow...
Age 11 to 14 Challenge Level:
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Ben's Game
Age 11 to 16 Challenge Level:
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
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?
Magic W
Age 14 to 16 Challenge Level:
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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.
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.
Reach 100
Age 7 to 14 Challenge Level:
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Neighbourly Addition
Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
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?
The Great Weights Puzzle
Age 14 to 16 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?
Window Frames
Age 5 to 14 Challenge Level:
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Latin Lilies
Age 7 to 16 Challenge Level:
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
Warmsnug Double Glazing
Age 14 to 16 Challenge Level:
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
Squares in Rectangles
Age 11 to 14 Challenge Level:
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?
Advent Calendar 2011 - Secondary
Age 11 to 18 Challenge Level:
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
NRICH is part of the family of activities in the Millennium Mathematics Project.