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?
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 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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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?
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
A Sudoku with a twist.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Two sudokus in one. Challenge yourself to make the necessary
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?
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
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 Sudoku with clues as ratios or fractions.
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 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?
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?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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 this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A Sudoku with clues given as sums of entries.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A pair of Sudoku puzzles that together lead to a complete solution.
This Sudoku, based on differences. Using the one clue number can you find the solution?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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...
You need to find the values of the stars before you can apply normal Sudoku rules.
If you are given the mean, median and mode of five positive whole
numbers, can you find the numbers?
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.
Use the clues about the shaded areas to help solve this sudoku
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you coach your rowing eight to win?
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. . . .
Find out about Magic Squares in this article written for students. Why are they magic?!