## Solutions

## 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.