Time

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?

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?

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.?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

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

Here's a chance to work with large numbers...