Two natural numbers have a sum of less than 100 and are greater than one.
John knows the product of the numbers and Jacob knows the sum of numbers.
The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'
If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.
If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?
A man has a barrel filled with oil that weighs 100 pounds, and then he puts something into it. Now the barrel weighs less than 100 pounds. What did he put in the barrel?