15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
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?
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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
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?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
This Sudoku, based on differences. Using the one clue number can you find the solution?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with clues as ratios or fractions.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Use the differences to find the solution to this Sudoku.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
A pair of Sudoku puzzles that together lead to a complete solution.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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 task encourages you to investigate the number of edging pieces and panes in different sized windows.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Four small numbers give the clue to the contents of the four surrounding cells.
A Sudoku with a twist.