How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?
How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it.
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!'
In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?