Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
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.
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.
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?
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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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. . . .
Four small numbers give the clue to the contents of the four surrounding cells.
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
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.