Other tags that relate to Sam Again
Triangle numbers. Addition & subtraction. Working systematically. Mathematical reasoning & proof. Factors and multiples. Permutations. Generalising. Visualising. Describing patterns and sequences. Combinations.There are 131 results
Broad Topics > Thinking Mathematically > Working systematically
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?
Tea Cups
Age 7 to 14
Challenge Level
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.
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?
Oranges and Lemons, Say the Bells of St Clement's
Age 11 to 14
Challenge Level
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
Teddy Town
Age 5 to 14
Challenge Level
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?
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.
Twin Line-swapping Sudoku
Age 14 to 16
Challenge Level
A pair of Sudoku puzzles that together lead to a complete solution.
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
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.
Games Related to Nim
Age 5 to 16
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
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.
Colour in the Square
Age 7 to 16
Challenge Level
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Pole Star Sudoku 2
Age 11 to 16
Challenge Level
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
More on Mazes
Age 7 to 14
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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".
Extra Challenges from Madras
Age 11 to 14
Challenge Level
A few extra challenges set by some young NRICH members.
An Introduction to Magic Squares
Age 7 to 16
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Counting on Letters
Age 11 to 14
Challenge Level
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Diagonal Product Sudoku
Age 11 to 16
Challenge Level
Given the products of diagonally opposite cells - can you complete this Sudoku?
Quadruple Sudoku
Age 11 to 16
Challenge Level
Four small numbers give the clue to the contents of the four surrounding cells.
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?
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.
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.
Maths Trails
Age 7 to 14
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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.
Alphabetti Sudoku
Age 11 to 16
Challenge Level
This Sudoku requires you to do some working backwards before working forwards.
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.
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?
Crossing the Bridge
Age 11 to 14
Challenge Level
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Number Daisy
Age 11 to 14
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 25?
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?
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.
Coins
Age 11 to 14
Challenge Level
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Simultaneous Equations Sudoku
Age 11 to 16
Challenge Level
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
Rainstorm Sudoku
Age 14 to 16
Challenge Level
Use the clues about the shaded areas to help solve this sudoku
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.
Diagonal Sums Sudoku
Age 7 to 16
Challenge Level
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?"
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.
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.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.