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.
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!'
Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.
Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee?
In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki