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?
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 values of the nine letters in the sum: FOOT + BALL = GAME
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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 the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
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?
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?"
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
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...
A pair of Sudoku puzzles that together lead to a complete solution.
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
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.
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?
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?
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?
A Sudoku that uses transformations as supporting clues.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
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?
Four small numbers give the clue to the contents of the four
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Two sudokus in one. Challenge yourself to make the necessary
This Sudoku, based on differences. Using the one clue number can you find the solution?
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 by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
This Sudoku combines all four arithmetic operations.
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.
Given the products of diagonally opposite 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?
A Sudoku with a twist.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!