Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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?
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 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 based on clues that give the differences between adjacent cells.
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?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku that uses transformations as supporting clues.
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...
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
A few extra challenges set by some young NRICH members.
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.
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
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?
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Charlie and Lynne 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?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
You need to find the values of the stars before you can apply normal Sudoku rules.
A pair of Sudoku puzzles that together lead to a complete solution.
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.
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. . . .
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Use the clues about the shaded areas to help solve this sudoku
This Sudoku combines all four arithmetic operations.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
If you are given the mean, median and mode of five positive whole numbers, can you find the 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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?