4 Aug 2005
The Survival Chamber
AD 2876. The nuclear war has exterminated almost the entire of human race. Only 400 people survive. The break-up - 100 cyborgs, 25 scientists, 65 programmers, 10 dictators, and 200 youngsters - 100 men and their sisters.
The scientists and dictators decide they must take up the cause of preventing the human race from becoming extinct. All the documentation and technology for SFC (SuperFast Cloning) has been destroyed. So, the only way left for them to have descendants is by making the young men and women mate among them and procreate. So, they put the 100 young men and their sisters - 100 in number - in the survival chamber. Everything inside the chamber is fully monitored by supercomputers so that it is always conducive to survival of all forms of life. Dictators love Chess, and scientists love Mathematics. Ergo, they decide to make this all into a game rather than a drab orgy.
The 200 subjects are not told about the purpose of the exercise until they are moved inside the chamber. Once inside, they are blindfolded and made to stand - men and women opposite each other, separated by good distance - in a random order. There are hundred rooms, designed to form a circle. The blindfolds are removed only when a person is inside either the room or the toilet. Now, the game is this - men are asked to choose their mating partners. Everybody is numbered - man 1 to man 100, woman 1 to woman 100. Each man is directed toward the place where women are standing, and the first woman whom he touches becomes his partner. Nobody is allowed to utter a word till all the pairs are formed. The dictators don't approve of incest. So, if the man happens to choose his sister for partner, both of them will be shot dead.
The entire process is monitored by cyborgs, so there's no place for tricks.
The probability of a man ending up choosing his sister for partner is 0.01. Out of all the combinations possible, there is exactly one that proves fatal for the human race - when each man chooses his sister. In such a case, all the pairs will be shot dead. So, inside the chamber, the survival of a person depends not on how fit he is, but solely on chance.
What is the best move for a man to ensure he survives?
The rooms are numbered in anticlockwise direction, and they are occupied according as men's numbers in the same order (man 1 and his partner occupy room 1, man 2 and his partner occupy room 2, and so on).
After the first round of choosing, the scientists decide that it's a better idea to enhance the gene pool. Now, the pairs need to change partners in a sequential order (clockwise in direction) and it should go on for another 49 times (after the first round, man 1 will have man 2's partner and man 100 will have man 1's, and so on). But the same rules hold - when a man ends up with his sister for partner, both of them will be shot dead. So, if a man is lucky enough that his sister is not among the next 49 men's partners, he will survive at the end and will have had 50 partners in total.
How many such combinations exist that will keep all of them survive at the end?
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