An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
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?
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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...
Use the differences to find the solution to this Sudoku.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
How many different symmetrical shapes can you make by shading triangles or 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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?!
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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. . . .
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.
Two sudokus in one. Challenge yourself to make the necessary
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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. . . .
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
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.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
A Sudoku with a twist.
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios.
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 man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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. . . .
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku with clues given as sums of entries.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
This Sudoku combines all four arithmetic operations.