A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
Calendars were one of the earliest calculating devices developed by civilizations. Find out about the Mayan calendar in this article.
Every day at noon a boat leaves Le Havre for New York while another
boat leaves New York for Le Havre. The ocean crossing takes seven
days. How many boats will each boat cross during their journey?
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
This month there is a Friday the thirteenth and this year there are three. Can you explain why every year must contain at least one Friday the thirteenth?
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When
did July 1st fall on a Monday again?
A bus route has a total duration of 40 minutes. Every 10 minutes,
two buses set out, one from each end. How many buses will one bus
meet on its way from one end to the other end?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
Great Granddad is very proud of his telegram from the Queen
congratulating him on his hundredth birthday and he has friends who
are even older than he is... When was he born?
N people visit their friends staying N kilometres along the coast.
Some walk along the cliff path at N km an hour, the rest go by car.
How long is the road?
Use the clocks to investigate French decimal time in this problem.
Can you see how this time system worked?
Which segment on a digital clock is lit most each day? Which
segment is lit least? Does it make any difference if it is set to
12 hours or 24 hours?
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
How far have these students walked by the time the teacher's car
reaches them after their bus broke down?
This article explains how Greenwich Mean Time was established and in fact, why Greenwich in London was chosen as the standard.
Here's a chance to work with large numbers...
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
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 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
At the time of writing the hour and minute hands of my clock are at
right angles. How long will it be before they are at right angles
Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?
Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
What can you say about when these pictures were taken?
Read this article to find out the mathematical method for working out what day of the week each particular date fell on back as far as 1700.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Two trains set off at the same time from each end of a single
straight railway line. A very fast bee starts off in front of the
first train and flies continuously back and forth between the. . . .
Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.
Not everybody agreed that the Third Millennium actually began on January 1st 2000. Find out why by reading this brief article.
In this matching game, you have to decide how long different events take.
The pages of my calendar have got mixed up. Can you sort them out?
If Tom wants to learn to cook his favourite supper, he needs to make a schedule so that everything is ready at the same time.
Can you rank these quantities in order? You may need to find out
extra information or perform some experiments to justify your
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you put these times on the clocks in order? You might like to arrange them in a circle.
Can you put these mixed-up times in order? You could arrange them in a circle.
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
Can you place these quantities in order from smallest to largest?
Use your knowledge of angles to work out how many degrees the hour
and minute hands of a clock travel through in different amounts of
Investigate the different distances of these car journeys and find
out how long they take.
A game for two or more players that uses a knowledge of measuring
tools. Spin the spinner and identify which jobs can be done with
the measuring tool shown.
My measurements have got all jumbled up! Swap them around and see
if you can find a combination where every measurement is valid.
Nirmala and Riki live 9 kilometres away from the nearest market.
They both want to arrive at the market at exactly noon. What time
should each of them start riding their bikes?
These clocks have only one hand, but can you work out what time
they are showing from the information?
These two challenges will test your time-keeping!
Mathematics has allowed us now to measure lots of things about eclipses and so calculate exactly when they will happen, where they can be seen from, and what they will look like.
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.
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?