Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 20-08-2008 18:24
20 August 2008:
THE SOLUTION:
Turn over any three slips of paper. Next continue to turn papers until you reach a number higher than the highest number on the first three slips of paper. This is the number you stop on and show your captor. If you are about to turn over all the papers, stop at (and choose) the last one turned. This system gives you maximum odds of escaping, which are slightly better than one in three.
a279;The ancient paths of Dr. Livingstone. Dr. Livingstone is traveling from Town A through Town B to Town C in the deepest heart of Africa. In how many ways can he travel, assuming that he does not travel a road more than once or through a town more than once? In other words, he doesn’t backtrack.
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 26-08-2008 23:39
26 August 2008:
THE SOLUTION:
a279;There are 6 ways to get from A to B and 4 ways to get from B to C. Using the multiplication principle we find 6 X 4 = 24 possible paths from A to C.
A stomach, a heart, a kidney, a brain, and a spleen are lined up in a neat row along a mad scientist’s table. In how many different ways can they be arranged in the row?
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 27-08-2008 23:13
27August 2008:
THE SOLUTION:
We have 5 organs. As we learned, the organs have 5! = 5 x 4 x 3 x 2 x 1 = 120 permutations.
An archaeologist wishes to visit Jerusalem, Damascus, Cairo, Baghdad, Nairobi, Meru, and Mombasa. Before he and his wife leave for the trip, his wife insists that they visit Mombasa last. In how many ways can their order of visits vary?
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 28-08-2008 23:18
28 August 2008:
THE SOLUTION:
Because the wife has chosen the last city, we are left with a permutation of 6 cities, which is 6! = 720 different
ways they can order their visits.
A movie star bearing a striking resemblance to Shannen Doherty has sixteen different-sized diamonds to string on a bracelet. In how many ways can this be done?
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 29-08-2008 22:53
29 August 2008:
THE SOLUTION:
a279;Diamond arrangements. We find (n - 1)! arrangements, given n different objects arranged in a circle. Thus, the movie star has an amazing 15! = 1,307,674,368,000 different possible arrangements of the diamonds on the bracelet. If diamonds were cheap, it would be very easy to give a different arrangement of the 16 diamonds to everyone on Earth and still have many more arrangements left over.
a279;Marble maze. You drop a marble into the maze in figure and it is pulled down by gravity. At certain points, the marble has a choice of taking one of two forks in the tunnel. These choices are marked by dots. Assume that each time the marble has a valid choice of tunnels, it is equally likely to choose either route. You win a neural stimulator that gives you ecstatic pleasure if you emerge at the tunnel marked “Win.”
What is the likelihood that you will win the prize?
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
Posts: 3552 Location: India Joined: 29.10.07 Thanks: 9 Thanked 158 times in 107 posts
Posted on 30-08-2008 23:43
30 August 2008:
THE SOLUTION:
One way to solve this maze puzzle is to realize that at each marked intersection (or decision point), the marble has a 50-50 choice (or 1/2 chance) of going right or left. There are three paths by which the marble can get to the winning exit (1-2-6-8, 1-2-4-6-8, and 1-3-5-4-6-8). All we need to do is multiply the 1/2 probabilities at each decision point along each path to find the likelihood of traveling a particular path. So for the three a279;paths we have (1/2 x 1/2 x 1/2 x 1/2) + (1/2 x 1/2 x 1/2 x 1/2 x 1/2) + (1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2). Thus, we find 1/16 + 1/32 + 1/64 which is about 0.11—only about an 11 percent chance of winning!
Sally is looking at a sushi menu. To make a single piece of sushi, she can choose tuna, squid, or shrimp, which can be either in the form of a roll or sliced. In addition, the piece may be either plain or coated with red, black, white, or green caviar. How many different pieces of sushi can Sally make?
"To catch me, you gotta be fast...
To beat me, you gotta be strong...
But to be me? Damn, you gotta be kiddin!!!"
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