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?
On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?
When the bus sets off there will be a bus
arriving from the other end, a bus due to arrive 10 minutes later,
a bus due to arrive 20 minutes later, a bus due to arrive 30
minutes later, and a bus just leaving at the other end which is due
to arrive in 40 minutes. The bus will meet all these buses and all
the buses that leave while it is travelling, that is, the buses
that leave 10, 20 and 30 minutes after it has set off. It will
arrive as another bus prepares to leave.
So the bus will set off as a bus arrives from
the other end, meet a bus every 5 minutes while travelling (7 in
all) and arrive at the other end as another is leaving.
If it is the first bus of the day, it will
only meet 4 buses on its way, the second bus of the day will meet
5, the third bus will meet 6, the fourth bus will meet 7, the buses
after the fourth one will all meet 7 except the last three - they
will meet 6, 5 and 4 respectively.
A bus in the middle of the day will either meet 7 or 9 depending
on whether you count the buses it meets at either end of its
journey. However the first and last bus will only meet 4 or 5
depending on whether you count the bus leaving as it arrives (in
the case of the 1st bus) or leaves (in the case of the last
Anna, PD and Emily from Ardingly College
Junior School thought of it like this:
... if it left the station at 3.40pm it would meet the ones that
left the station within 40 minutes before and after it and the one
that left at the same time as it.
Heather from Stow Heath Junior School noticed
If we start counting as the first bus leaves for the day then it
will not see another bus until it is half way along it's route.
Laura and Harriet from The Mount School
explained it as follows:
Bus A and B set out at the same time, then 10 minutes later
buses C and D set out. At this point none of the buses have
advanced enough to meet another. Then, after 20 minutes, two more
buses, E and F set out, and A and B meet. After 25 minutes A will
meet D. 30 minutes into the cycle, A will meet F. G and H will set
off. After 35 minutes A will meet H. Then at 40 minutes, the cycle
will be complete, and A will meet one final bus, J, which is
setting out. If bus A had been the first bus to set off, it would
meet 5 other buses. If bus A had set off while the cycle was taking
place, it would meet 8 other buses.
Well done to all of you who managed to crack