For some reason some people in group1 have further split people in group2, for instance (A[n/2 +1],…,A[3n/4]) and (A[3n/4 + 1],…, An)… these members of group1 may go if the first half of group2 is on the trip, but they definitely cannot be made to go even if there is one person from the second half (remember the numbers are not exact but a highly simplified situation which is to be used only as an example for understanding the problem).
The members in group2 also have a similar classification, however they have the habit of reluctantly agreeing to do things that they don’t want to do for certain trivial favors like having the window seat which are easily achievable. But as a further complication some members of group2 from the second subset actually would go on the trip only if those particular members of group1 who would not come if they were on the trip, were on the trip.
One more constraint in the groups was that the requirement was that every An in the group had another An who should be in the trip otherwise they cannot come on the trip. For example let us say A1 wanted A2 to come on the trip, but A2 would come only if A3 also came, but then A3 would come only if A4 came. Even if there was a slight doubt that one of the link could be broken, then the whole group would have a cascading effect sort of.
A, who knew all this, made a very small subset made up of members of both groups – 1 and 2 who managed to tolerate each other. But the news being news and especially since A tried to keep it a secret spread like wildfire. In fact, even people who were outside the big set of all friends got to know of this planned trip. This had its own positive and negative aspects which we shall proceed to explain as constraints of the problem as follows.
Some members of group1 called in some people who were outside the initial set (A1,…,An)… let us call them An-m (A1-1, A1-2,A2-1,A2-2, A2-3 and so on…) where n denotes the nth friend from the original set and m denotes the mth friend of the nth individual who did not belong in the original set but belongs to the universal set. So what happens now is that An-m would come on the trip only if A and the rest of A’s set accepted An-m. In case they did not accept that An-m, then he would not come. Since none of An’s knew any of the An-m’s apart from that particular An, A assumed that no one would have any issues with that. But that was not to be. Some particular An’s who had An-m’s of their own, could not tolerate An-m’s of other An’s. But since the An-m’s were committed to on the trip because of A’s eagerness, the An’s now posed a new condition that those particular An’s would come on the trip only if the corresponding An-m’s also came on the trip.
Some members of group2, feeling that some other members of group2 would come only if their An-m’s would come and their An-m’s could come only if there were people – either An’s or An-m’s – with some special characteristics were on the trip. In fact this set of people with special characters can come only if there were some particular An with these special characters. So if this particular An with special characteristics did not come on the trip then the other special characteristic persons – An or An-m’s – will not come on the trip.
There were some developments also which caused the set (A1-An) to run around like a batch of scared sheep inside an enclosure.
Development1: Some rumor in the form of a news of an impending doom was given by a soothsayer. As all soothsayer predictions go, this one was also unverifiable, but caused major agitation among some superstitious members in the (A1-An) set. The An’s that were affected would come on the trip if the news was verified to be untrue. The others were unaffected and were classified as brash and adventurous by those affected (though this classification bears no relevance to the solution, it is given here to keep options open for a sequel).
Development2: The one particular An who had special characteristics was not able to go on the trip because another particular An was not able to make it on the trip for unquoted (but irrelevant to the problem) reasons. So this made sure that the others with the special characteristics also could not go on the trip.
Further complication:Now, one of the An’s thinking that the persons with special characteristics can still come if some random person with similar special characteristics was also in the trip. But unfortunately all that he had done was adding an An-m as his dependent causing a further knot in the already knotty constraints list.
Now A is faced with the dilemma of the decision. Of course going all alone on the trip is not a very exciting option. So he has to have some An along with him. So the possible solutions are:
b) A should have a no-confidence motion at his house where he would give huge sums of money as bribes to members from group1 and group2 to defect from their groups into the other group and add to his bankruptcy.
c) A should go and train for the Olympics swimming and diving championships in the swimming pool that is directly below the balcony of his pool facing apartment and not worry about petty things in life, but focus on getting gold for his country.
d) A suddenly finds his job very interesting and his Boss to be an angel and starts working on a new initiative for his company’s plans for world domination
e) A should get married and add another dimension to his set (A1,...,An)
f) A should go to the Himalayas for the vacation
g) A should go to the Himalayas permanently
h) None of the above. I, like all other An’s, have a unique solution to the problem.
