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?
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.
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.
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 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?
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?
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 total.
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.
A pair of Sudoku puzzles that together lead to a complete solution.
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
A Sudoku with clues as ratios or fractions.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
A few extra challenges set by some young NRICH members.
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
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!
Four small numbers give the clue to the contents of the four surrounding cells.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Use the differences to find the solution to this Sudoku.
A Sudoku with a twist.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
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?
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?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
This Sudoku requires you to do some working backwards before working forwards.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
A Sudoku with a twist.
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.