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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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. . . .
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?
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 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?"
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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 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.
Given the products of adjacent cells, can you complete this Sudoku?
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 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?
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 Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
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 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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
Given the products of diagonally opposite cells - can you complete this 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.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
A Sudoku with a twist.
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. . . .
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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...
Two sudokus in one. Challenge yourself to make the necessary
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 pair of Sudoku puzzles that together lead to a complete solution.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.