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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
By selecting digits for an addition grid, what targets can you make?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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 need to find the values of the stars before you can apply normal Sudoku rules.
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
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 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.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
A Sudoku with clues as ratios.
A Sudoku with clues as ratios.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
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?
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
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.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
A Sudoku with a twist.
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.
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.
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?
A Sudoku with a twist.
This Sudoku requires you to do some working backwards before working forwards.
In this game you are challenged to gain more columns of lily pads than your opponent.
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?
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.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?