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 two
trains. How far does Sidney fly before he is squashed between the
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
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?
Hayley of Lytham St Annes High School sent in
a beautifully presented word processed solution which we have
re-produced here. She did more than the question asked for,
calculating how long each segment is lit up in a day rather than
simply saying which is lit up for the most time and which for the
least time. In the best mathematical style Hayley first set up her
notation. Another very good solution was sent in by Helen of
Maidstone Girls' Grammar School who used the same notation.
In doing mathematics in real life (as opposed
to answering text book or exam questions) the first step is to
define the problem precisely and in so doing you must state clearly
what is being assumed. This is exactly what Hayley did, she assumed
that, until ten o'clock, rather than having no number lit up for
digit A, a zero is put there. If you make different assumptions you
get different versions of the problem which will, in many cases,
have different answers.
Segments 3 and 6 on digit A are on 24 hours a day.
There is either a 0 or a 1 for digit A, and these two segments are
lit for both a 0 and a 1.
It is easy to discount all other digits as they all cycle round
every digit, or digits 1-5, and every segment is turned off at some
time in this way.
Least Used Segment
Segment 4 on digit A is never turned on, as it is not contained
in either the 0 or 1.
You can discount the other segments as they are all turned on at
From the following tables you can tell that the segment on for
the most time is segment 3 on digit A. As this digit can only have
a 0, 1, or 2, this segment is on all the time.
The least used segment on the 24 hour clock is segment 5 on