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?
A Sudoku based on clues that give the differences between adjacent cells.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
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?
Two sudokus in one. Challenge yourself to make the necessary
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku that uses transformations as supporting clues.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
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?
A Sudoku with clues as ratios.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A Sudoku with clues as ratios or fractions.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
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
How many different symmetrical shapes can you make by shading triangles or squares?
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 Sudoku combines all four arithmetic operations.
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 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. . . .
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative 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.
A Sudoku with a twist.
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
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?
A Sudoku with clues given as sums of entries.
Label this plum tree graph to make it totally magic!
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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.