Puzzles 7

Questions1. A man is awake night after night without getting a wink of sleep, and yet he doesn’t feel tired. How can this be?

2. Billy has just bought a new car. On his way home from work he is so excited at the prospect of showing off his new car to his girlfriend that he isn’t paying attention. He goes past a red light without stopping, bumps into somebody in front of him and then turns into a “No Entry” road. Despite these actions, an on-duty police officer who is observing him makes no attempt to stop him. Why?

3. Billy’s car cost him £2,000 plus half its price. How much did it cost?

4. A con-man offers a poor beggar an earthenware jug containing a liquid that he swears will turn everything it comes into contact with into pure gold. The beggar refuses the offer. Why was the beggar not deceived?

5. If only one of these statements is true, how many brothers have I got?

‘I’ve got ten or more brothers.’

‘I’ve got less than ten brothers.’

‘I’ve got at least one brother.’



1. He works night shifts and sleeps during the day.

2. Billy was walking home. His new car had been delivered to his house.

3. £4,000. Use algebra: Let x = the price of Billy’s car. Then solve the equation x = (1/2)x + 2000.

4. If the con-man had been telling the truth, the jug would itself have been
turned to gold.

5. None. ‘I’ve got less than ten brothers’ is the only statement that can be
true by itself. What’s more, if it’s the only statement which is true, this
rules out having at least one brother at the same time, and so zero brothers is
the only possibility remaining.

About Melluvahess

My name is Sean Maguire and I am the founder of Maths Made Elementary. I provide expert one-to-one maths tuition within North London to lower and upper secondary level students studying at Key Stages 3 and 4. For more information about me, and the services I offer, please check out my website www.mathsmadeelementary.co.uk
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