As I am nearing the end of the book "Fermat's last theorm" I am starting to feel a li'l enlightened (dunno why :P). I have started reading mathematical puzzles on internet, also started devoting some time thinking about a few Number Theory axioms,rules. So decided to keep everyone else also in loop and share any thoughts on any new mathematical topics,statements i come across. This new post is entirely dedicated to such findings. I will keep on updating the post with new things i learn or find on the web. Most of them should be known to you but it doesnt hurt to go over them yet another time ;). Please post anything you want to add in comments section and I will edit the post :P. Lets start rocking.[1] 25 + 27 + 29 + 53 + 54 = 52 + 72 + 92 + 35 + 45
Did you know the above equality?
[2] A very well known puzzle. Most of you must have heard of the puzzle but do you know the solution?
Imagine that you are a contestant on a television game show. You are shown three large doors. Behind one of the doors is a new car, and behind each of the other two is a goat. To win the car, you simply have to choose which door it is behind. When you choose a door, the host of the show opens one of the doors you have not chosen, and shows you that there is a goat behind it. You are then given a choice; you may stick with your original choice, or you may switch to the remaining closed door.
What should you do to maximize your chances of winning the car?
PS- Special mention of Mr. Suhas Rao who introduced me to the book and helped me realize the world beyond eating and sleeping :).
4 comments:
To the second problem a very nice concept has been shown in the recent movie "21". The concept of "Variable Change" or the "Monty Hall Problem / Paradox".
Because there is no way for the player to know which of the two unopened doors is the winning door, most people assume that each door has an equal probability and conclude that switching does not matter. In fact, in the usual interpretation of the problem the player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3. Switching is only not advantageous if the player initially chooses the winning door, which happens with probability 1/3. With probability 2/3, the player initially chooses one of two losing doors; when the other losing door is revealed, switching yields the winning door with certainty. The total probability of winning when switching is thus 2/3.
Awesome concept really !!
gg dada but couldnt understand your concept. I calculated probability on the basis of simple maths.
The Monty Hall problem has one catch line as well I guess. Whenever you pick the first door ( with the car behind it ) you tend to lose if you switch. Correct me if I am wrong.
I was just thinking that what could be the probability of me using the concept of variable change ( i.e. switching when asked to ) and winning in the end; In other words, since I am switching, what is the probability that I will not choose the door with the car behind it the first time, and win the game.
you are rite my friend :P
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