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?
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
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 models can you find which obey these rules?
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?
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?
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?
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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.
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....?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many different triangles can you make on a circular pegboard that has nine pegs?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
An activity making various patterns with 2 x 1 rectangular tiles.