Use the differences to find the solution to this Sudoku.
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?
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
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...
How many different symmetrical shapes can you make by shading triangles or squares?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
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?
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?
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?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Label this plum tree graph to make it totally magic!
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?
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?
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 Sudoku with clues as ratios.
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. . . .
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
A Sudoku with a twist.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?