Random Puzzles 

Workings

Hint
Try this with a real board.

Answer
5 queens are required.

Workings

Hint
Who is in last place?

Answer
This cannot happen, you cannot overtake the person who is in last place, as there is no-one behind them!

Ovetaking = passing someone who is ahead on the same lap, this is a change of position, e.g. 4^th moves up to 3^rd.

Lapping = passing someone who is a full lap behind, this isn't a change of position, e.g. 4^th stays 4^th.

Workings

Hint
When does the clock strike just once?

Answer
1.30 in the morning.

The initial single strike was at 12.30.

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter which has a problem with the middle row of letters, which print spaces instead. The letter should have read:
Dear Sir,

I recently visited one of your outlets to buy one of your typewriters. However, as you can see I am having a small problem.

The middle row of the keyboard appears to be faulty.

I would be very grateful if you could despatch a replacement by return post. Failing this, could you please send an engineer to resolve this problem as a matter of urgency.

Yours faithfully,

Mrs Middins.