Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
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?
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 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?
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?
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?
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.
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.
A Sudoku based on clues that give the differences between adjacent cells.
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
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?
A Sudoku with clues as ratios or fractions.
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 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?
A Sudoku with a twist.
A Sudoku with clues as ratios.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square 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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
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 sudoku requires you to have "double vision" - two Sudoku's for the price of one
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A Sudoku with clues given as sums of entries.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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
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...
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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. . . .
Can you coach your rowing eight to win?
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?