If three ill-matched heterosexual couples sit around a table in such a way that no one is sitting next to their spouse and maintaining the traditional boy-girl alternation, as was discussed last week, there is only one possibility (or two if they are considered different mirror-symmetrical arrangements), in which the members of each pair occupy diametrically opposite seats. But if the formal boy-girl alternation is not respected, there are several provisions compatible with marital incompatibility (how many exactly?).
Regarding the more complex problem of the round table with n evenly spaced chairs in which n people are going to sit sequentially (see full statement in the previous installment), here is what Manuel Amorós comments:
“The first thing that has occurred to me is to consider the successive positions reducing them to modulo n. Only in the case that this series of addends goes through the system of complete remainders of n, each one will occupy a chair, if not, there will be coincidences. I think this only happens when n = 2^k (that is, when it is a power of 2). In any other case, there are overlaps, and it cannot be achieved.”
conjugal combinatorics
Let’s continue with the three ill-matched heterosexual couples, whose members arrive at the restaurant separately (as befits their disagreement). If the six people arrive one by one, how many must have arrived, at least, so that there is certainly at least one married couple in the restaurant? And for there to be a concrete marriage? And so that there are with certainty at least two people of the same sex? And so that there are certainly at least two women?
If instead of sitting at the table based on their disagreements, they do so randomly, what is the probability that a specific woman sits next to her husband? And that of at least one married couple occupying adjoining chairs? And the one that the three marriages do? And the one that everyone’s wish is fulfilled by pure chance, that is, that no one sits next to her spouse?
The women are called Ana, Berta and Carolina, and the men, Daniel, Ernesto and Fernando. During dinner they drink 3 liters of wine. One of the people is a teetotaler. Daniel drinks the same as the three women together. Ernesto drinks twice as much as his wife. Carolina drinks twice as much as another of the women. The one who drinks the most is Fernando, and the one who drinks the least is his wife. What is the name of Daniel’s wife? And the rigorous meta-question: is this information enough to give a safe answer? Other: could the same answer be obtained with less information?
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#controversial #dinner