Four small numbers give the clue to the contents of the four
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Two sudokus in one. Challenge yourself to make the necessary
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Solve the equations to identify the clue numbers in this Sudoku problem.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
A Sudoku with clues given as sums of entries.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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. . . .
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A Sudoku with clues as ratios.
Use the differences to find the solution to this Sudoku.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This Sudoku combines all four arithmetic operations.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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.
A Sudoku that uses transformations as supporting clues.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Follow the clues to find the mystery number.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Investigate the different ways you could split up these rooms so
that you have double the number.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.