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
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.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
What could the half time scores have been in these Olympic hockey
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.
Follow the clues to find the mystery number.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you replace the letters with numbers? Is there only one
solution in each case?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you substitute numbers for the letters in these sums?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
What happens when you round these three-digit numbers to the nearest 100?
The pages of my calendar have got mixed up. Can you sort them out?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In this matching game, you have to decide how long different events take.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you find all the different ways of lining up these Cuisenaire
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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 dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
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 different triangles can you make on a circular pegboard that has nine pegs?
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. . . .
Find out what a "fault-free" rectangle is and try to make some of
This Sudoku, based on differences. Using the one clue number can you find the solution?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Find out about Magic Squares in this article written for students. Why are they magic?!