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.
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?
A Sudoku with a twist.
Two sudokus in one. Challenge yourself to make the necessary
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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?
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?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
A Sudoku with clues as ratios or fractions.
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 as ratios.
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues given as sums of entries.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
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.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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.
Four small numbers give the clue to the contents of the four
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
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 clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
Solve the equations to identify the clue numbers in this Sudoku problem.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A few extra challenges set by some young NRICH members.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Find out what a "fault-free" rectangle is and try to make some of