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?"
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. . . .
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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"?
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?
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?
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...
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the products of adjacent cells, can you complete this Sudoku?
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 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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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.
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.
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?
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?
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.
The clues for this Sudoku are the product of the numbers in
Given the products of diagonally opposite cells - can you complete
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The idea of this game is to add or subtract the two numbers on the
dice and cover the result on the grid, trying to get a line of
three. Are there some numbers that are good to aim for?
A pair of Sudoku puzzles that together lead to a complete solution.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Four small numbers give the clue to the contents of the four
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Use the clues about the shaded areas to help solve this sudoku
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
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. . . .