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.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
Can you find all the different triangles on these peg boards, and
find their angles?
What happens when you try and fit the triomino pieces into these
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you cover the camel with these pieces?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many models can you find which obey these rules?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In this matching game, you have to decide how long different events take.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Try this matching game which will help you recognise different ways of saying the same time interval.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Find out what a "fault-free" rectangle is and try to make some of
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you find all the different ways of lining up these Cuisenaire
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different triangles can you make on a circular pegboard that has nine pegs?