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.
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 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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
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.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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?
Given the products of diagonally opposite cells - can you complete this 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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
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.
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Label this plum tree graph to make it totally magic!
Charlie and Abi 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 think?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Use the clues about the shaded areas to help solve this sudoku
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Two sudokus in one. Challenge yourself to make the necessary