Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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?
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?
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. . . .
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Given the products of adjacent cells, can you complete this Sudoku?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?"
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?
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A pair of Sudoku puzzles that together lead to a complete solution.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
You need to find the values of the stars before you can apply normal Sudoku rules.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku with clues as ratios.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku that uses transformations as supporting clues.
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?
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Four small numbers give the clue to the contents of the four
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
Two sudokus in one. Challenge yourself to make the necessary
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
This Sudoku combines all four arithmetic operations.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
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?