### Speedy Sidney

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 two trains?

### Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

### Digital Times

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?

# Hands Together

##### Stage: 3 Challenge Level:

Sometime during every hour the minute hand lies directly above the hour hand.

During the twelve hours of the day the hands are together exactly 11 times. This means that they are together at 12 o'clock and every 1 hour and 5$\frac{5}{11}$ minutes afterwards. Extending this to between 4 o'clock and 5 o'clock the hands must be together at 21 and $\frac{9}{11}$ minutes past 4 o'clock or (putting that another way) 4:21:49 and $\frac{1}{11}$ of a second.