Here are some problems that require the solver to use only logic to find a beautiful solution.
You are placed in a locked room and given a clear glass bottle completely filled with pure water. The bottle has a very strange shape and when holding it you see that it has no symmetry that you can see. It is closed with a screw on aluminum cap. If you unscrew the cap you can pour water out. You are wearing your normal street clothes and have no tools or devices other than what normally carry with you. If you do not return the bottle exactly half full of water by the next morning you will have to eat brussel sprouts at every meal for the rest of your life.
How can you return the bottle exactly half full of water?
Upstairs in a house are three rooms, each of which is lit with a single standard light bulb in a table lamp. Downstairs is a panel with the three corresponding light switches. You don't know which switch corresponds with which light. The lights are currently all off. You can’t see from downstairs which switch and light correspond as the three rooms are out of sight of the panel.
How can you determine which switch turns on which light without going upstairs more than once?
You have two bottles of pills. One is labeled "A" and the other "B". There are 15 pills in each bottle. In order to stay alive you must take one of each pill every morning for 15 days. If you take more than one of each on any day you will die. You pick up the "A" bottle and shake out a pill. Then you pick up the "B" bottle and, OOPS, you shake out two "B" pills. You now have three pills in the palm of your hand. The pills look identical. It takes 30 days to get more pills.
Explain how to stay alive.
Three missionaries and three cannibals are on one side of a river with a rowboat. The boat can hold only two people at a time. All three missionaries and one of the cannibals are able to row the boat. The cannibals will not kill and eat the missionaries as long as there are an equal number or more missionaries with the cannibals.
How can all six people get safely to the other side of the river?
A monk started up a mountain to have an audience with the Dali Lama. He began his journey at exactly 6 AM and arrived at the top at 6 PM. Along the way he stopped a number of times to rest and once to eat his meager meal. The next morning, at 5 AM he had his audience with the Dali Lama. Then he packed a small lunch and began his trip down the mountain at exactly 6 AM. Again he stopped a few times to rest and once to eat his lunch. He arrived at his original starting point at 6 PM.
Is there any place on the mountain that the monk is at exactly the same place at the same time on both days? Explain.
Five prisoners were due to be executed the next morning. The warden, a sporting man gave them a chance to save some of them. The next morning they must line up as follows: Prisoner 1: Nose and toes to wall. Prisoner 2: Right behind Prisoner 1 looking at the back of his head. Prisoner 3: Right behind Prisoner 2 looking at the back of his head. etc. The warden would then place either a black or white hat on each prisoner's head. Starting with Prisoner 5 (who could see the four hats in front of him, but not his own), each prisoner, in turn, must say either Black or White. If he correctly names his hat color he lives. Else he dies.
What strategy should they use to save the greatest number? Explain.