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.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
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?
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.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the clues to colour each square.
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....?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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 trains can you make which are the same length as Matt's,
using rods that are identical?
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
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
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 find all the different ways of lining up these Cuisenaire
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.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you find all the different triangles on these peg boards, and
find their angles?
Find out what a "fault-free" rectangle is and try to make some of
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.