## Solutions

## The Treasure Chest

There is a chest in front of you. The chest contains a number of pouches. In each pouch there is the same number of coins. The total number of coins in the chest is between 150 and 200. Each pouch contains more than one coin and there is more than one pouch in the chest. If you knew the number of coins in the chest you could tell me how many pouches there are in the chest and how many coins are in one pouch. So how many coins are in the chest?

169 coins

The number of coins must be a square of a prime number, otherwise there is no unique solution. It must be a square number, otherwise the number of coins per pouch and the number of pouches would be interchangeable. If the number of coins per pouch were not a prime number, the total number could be decomposed into two other factors. Since the only square of a prime number between 150 and 200 is 169 and the square root of 169 is 13, this must be the solution.

## Integer Sequences

Determine the next number that logically continues the sequence:

68

_{n+1}= 2(x

_{n}– 2)

## Two Villages

You are at a fork in the road. Unfortunately, the signpost has been blown away. You know only that one path leads to a village of pathological liars, and the other to one of vehement truth tellers. At the fork there is a person from one of the villages. What one question can you ask the person to tell you which road leads to which village?

On which path is the village you come from?

The person will always point the way to the village of truth. If they are from that village, they will always tell the truth, and therefore point there. If they are from the other village, they must lie, and therefore also point to the path of truth.

## Shriveling Melons

A truck is transporting melons. At the start of their journey, the melons weigh one ton. The water content is 99%. Over the course of the trip, the melons lose water, ending up at 98% water contents. What does the load now weigh?

The melons now weigh 500kg.

The proportion of dry mass doubles from one to two percent. But since the absolute dry mass is constant, the total mass in the end must to be half of the mass in the beginning.

## The Hunting Dog

A hunter walks 2km from his lookout to his home at a constant speed. His overzealous dog runs ahead and arrives before him. From there, the hunting dog immediately returns to the hunter. When he reaches the hunter he turns back and runs home. This goes on, back and forth, until the hunter arrives home. What distance has the dog run in total if he moves at thrice the speed of the hunter?

The dog has run 6km.

As both creatures spend the same time in motion, and the dog has thrice the speed, the dog covers three times as much distance as the hunter. 3 times 2km are 6km.