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?
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.
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. . . .
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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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?
A pair of Sudoku puzzles that together lead to a complete solution.
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.
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?
A Sudoku with clues as ratios.
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?
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A Sudoku that uses transformations as supporting clues.
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...
Four small numbers give the clue to the contents of the four
This Sudoku combines all four arithmetic operations.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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. . . .
A Sudoku with a twist.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A Sudoku with clues as ratios or fractions.