Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
How many models can you find which obey these rules?
Can you use the information to find out which cards I have used?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you find all the different ways of lining up these Cuisenaire
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
What is the best way to shunt these carriages so that each train
can continue its journey?
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
How many trains can you make which are the same length as Matt's, using rods that are identical?
What happens when you try and fit the triomino pieces into these
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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 6 in the circles so that each number is the
difference between the two numbers just below it.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Investigate the different ways you could split up these rooms so
that you have double the number.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold