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?"
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the 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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of diagonally opposite cells - can you complete
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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...
The clues for this Sudoku are the product of the numbers in
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
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.
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?
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?
Charlie and Lynne 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
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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.
Four small numbers give the clue to the contents of the four
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
A pair of Sudoku puzzles that together lead to a complete solution.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Use the differences to find the solution to this Sudoku.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
How many different symmetrical shapes can you make by shading triangles or squares?
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
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
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.
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.
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. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?