Brain teaser #1 You have two ropes of equal length. Both burn in 60 minutes. You have a matchbox and you can light the ropes at any time from any end. You do not have anything other than the ropes and a matchbox. How will you calculate 45 minutes?
Brain teaser #2 You have three boxes: Apples, Oranges, Apples + Oranges in them. All three are labelled incorrectly. You can open only one box to see what’s in it. How will you tell the correct order?
Answer #1 Light the first rope from both ends and the other rope from one end. The former rope will incinerate in 30 minutes (You have a count of 30 minutes now). The latter rope still has 30 minutes left. The moment the first rope has finished burning, light the other end of the second rope and it will incinerate in 15 minutes. It took you 45 minutes.
Answer #2 Open any box, e.g we open the box ‘Apples’. Suppose we see ‘Apples + Oranges’ in it. Now from the other two boxes, one contains Apples and the other contains Oranges. The box ‘Oranges’ cannot have Oranges, because all of the boxes are labelled incorrectly, so obviously it contains Apples. Thus the last box contains Oranges.