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?
The King showed the Princess a map of the maze and the Princess was
allowed to decide which room she would wait in. She was not allowed
to send a copy to her lover who would have to guess which path to
follow. Which room should she wait in to give her lover the
greatest chance of finding her?
On a clock the second, minute and hour hands
are on the same axis. How many times in a 24 hour day will the
second hand be parallel to either of the other two hands?
This is an extension of the
problem from November 1996. You might like
to look at the solution
to that problem.
Ling Xiang Ning has cracked this tough nut,
well done Xiang Ning! Here is his answer:
First consider the second and minutes hands. In one hour, the
minute hand makes one revolution and the second hand goes round 60
times. This means that, in one hour, the second hand passes over
the minute hand 60 - 1 = 59 times and the two are also in line (but
with 180 degrees between them) 59 times. In 24 hours the two are
parallel (24*59*2 = 2832) times.
Now consider the second and hour hands. In one hour the hour
hand makes 1/12 revolution while the second hand makes 60
revolutions. So, in 24 hours, the hour hand makes (24*1/12 = 2)
revolutions and the second hand goes round (24*60=1440) times. This
means that, in 24 hours, the second hand passes over the minute
hand 1438 times and the two are also in line (but with 180 degrees
between them) another 1438 times. In 24 hours the two are parallel
All three hands, the second, the minute and the hour hands, are
parallel 4 times in every 24 hours, once if they are aligned at 12
midnight and then at 06.00 and 12.00 and at 18.00.
So the second hand is parallel to either the minute hand or the
hour hand [(2832 + 2876) - 4 = 5704] times.