Ancient Coins

Suppose I show you two ancient coins. The first one is dated 51 B.C., the second one is marked George I. Which one is counterfeit?

Both of them. People who lived 51 years before Christ didn’t know about Jesus yet. Also, when king George I was ruling, he was the first king with this name, and thus was regarded simply as George.

Seven Bridges

This is a map of old-time Kongsberg. The green shapes are bridges which connect the different parts of the city. Can you find a path through the city which goes through every bridge exactly once?

No, you cannot. Notice that, except for the first city and the last city section you finish, the number of bridges used in every other section is even. However, there are three sections with an odd number of bridges, and therefore you cannot use all bridges exactly once.

Mountain Hike

A man decides to climb a mountain. He starts at sunrise from the bottom of the mountain and arrives on the top at sunset. He sleeps there and on the next day he goes back the same way, descending at higher speed. Prove that there is some point of his path, on which the man will be at the same time on both days.

Imagine a second man who starts climbing from the bottom of the mountain on the second day and following the first hiker’s first day movements. At some point the first and the second hiker will meet each other, and this will be the point you are looking for.

Six Glasses

Six identical glasses are placed in a row on the table – first three filled with water, and then three empty ones. Can you move just one glass, so that empty and full glasses alternate?

Take the second full glass, pour all of the water into the second empty glass, and then put it back in its place.