Perplexing Math

Answers anyone?

• You throw three darts onto the surface of a globe, each from a randomly chosen direction. What is the probability that all three darts are in one hemisphere?
• You are a bug sitting in one corner of a cubic room. You wish to walk (no flying) to the extreme opposite corner (the one farthest from you). Describe the shortest path that you can walk.
• An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?
• There are ten gnomes who have gotten themselves into quite a predicament. They are in the dungeon of a castle of a tyrannical king. Despite the evilness of the king, he has a silver lining in his heart. He has given the gnomes a chance of survival. Here is the offer: The King lines the gnomes up in a single-file row. This means that the tenth gnome sees the back of the person in front of him, and there is no gnome behind the tenth gnome. The ninth gnome has the tenth gnome behind him and the eighth gnome directly in front of him, and so on. Finally, the first gnome has the second gnome directly behind him, but there is no one in front of the first gnome. The king has a large bag full of many black hats and many white hats. There is not necessarily the same number of black hats as white hats. The king randomly reaches into his bag and places a hat on each of the gnomes. This means that the tenth gnome can see everyone’s hat except his own, the ninth gnome can see everyone’s hat except his own and the tenth gnome’s hat, and so on. The first gnome can see no one’s hat. The king then takes out his gun and puts it to the temple of the tenth gnome. The king asks the gnome, “What color is your hat?” If the gnome answers correctly, he lives and gets freed from the dungeon. If he does not, he dies. He continues up the line in this progression. However, before placing the hats on the gnomes, he allows the gnomes to meet as a group and discuss a strategy to save as many of the gnomes as possible. Imagine that you are one of these gnomes. What strategy would you develop? How many gnomes can you guarantee to save?  REMEMBER: When it is your turn to say the color of your hat you must ONLY say “white” or “black.” If you say anything else, the king will shoot you and all of the remaining gnomes.

Slumber Slain

Ok, so I haven’t written in ages. This time around I don’t even have a good excuse. Or maybe I do, but oh well. I’d rather sound like a slacker. Helps keep the expectations down, and life’s been teaching me a fair bit ’bout that lately. Gee tagged me, and so here goes- eight random facts about me.

1. I love cinema: Adore it, live it. There is something utterly powerful about what film can achieve. If I didn’t hate ‘development’ jargon so, I’d say the only thing capable of changing paradigms is great cinema. And woohooooo I’m getting to make a film. Life is good.
2. I know precious little: Yupsie daisy. I’m surrounded by people who think I’m well read, articulate and really original in terms of ideas. They couldn’t be more wrong. I’m as uninspired as they come, feed off my plate, live within my framework and am really happy just getting-by most times.
3. I believe in the Matrix and in magic: I do. I know spells work and I know there is something incredibly fabricated about the world we live in. For that matter, I also believe that dinosaurs exist in a lost islet somewhere wrapped in an envelope of slow-time. And no its not just Harry Potter, Jurassic Park or Reeves. Its about a manner of thinking. The metaphysical, that we all like to deny.
4. I love my gadgets: No in fact I’m obsessed. I’d feel desperately lonely without my phone despite not having anyone to call. I miss my iPod. My laptop is so customized only I know how to use it. I don’t like being called a techno-freak but people not taking computer security seriously bothers me. Just as not being able to tell flac from aac really upsets me.
5. Thunderstorms: Thunderstorms in my head still make me want to crawl under the bed. I don’t know what to make of that. Maybe I need a therapist. Tsk Tsk…
6. Cartoons: Peanuts, Calvin and Dilbert are the greatest political philosophers of all time. Period. Else I bite off your head.
7. Courage: I believe I will someday find a bottle full I can swallow. Maybe it will be green and golden. Ho hum.
8. I love cigarettes: Ok,I know. I do. I like adding clouds to my mind. Can’t help.

And oh, take a look at Pikey’s post and pick up the tag if you feel like. Its hard enough to blog without tagging…Sob.