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?
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 task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
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?
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?
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.
A pair of Sudoku puzzles that together lead to a complete solution.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
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?
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
A Sudoku based on clues that give the differences between adjacent cells.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
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.
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
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 Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
A Sudoku that uses transformations as supporting clues.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This Sudoku combines all four arithmetic operations.
A Sudoku with a twist.
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?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
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?
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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!
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
How many different symmetrical shapes can you make by shading triangles or squares?
Solve the equations to identify the clue numbers in this Sudoku problem.
This Sudoku requires you to do some working backwards before working forwards.