The hidden destiny of an Ecuadorian, if the Latin adage in nomen omen If true, as was suggested last week, it could be “aeronautical”, a surprising anagram of the word “Ecuadorian”. And if we talk about an alleged hidden message in the letters of a name, we cannot fail to mention the famous derogatory anagram that André Breton composed by rearranging the letters of “Salvador Dalí”: Ã vida Dollars. (Could you compose other allusive anagrams with the letters of some famous names?)
As for the now classic self-referential logic puzzle “How many letters are there in the correct answer to this question?”, the “official” answer, and the simplest, is “Five.” . By the way, in a magazine whose name I don't want to remember, they published this riddle with the answer “four”, which gives rise to the usual meta-problem: What do you think was the reason why they gave such a solution? absurdity to a widely known riddle?
The answer “Five” may seem unique, but it is not, and our regular commentator Bretos Bursó gives two other equally valid ones: “Half of forty-two” and “Double of seven.” To which we could add, along the same lines, others of the type “There are exactly twenty.” And, on the other hand, less precise but not incorrect answers are also valid, such as “Less than twelve.”
Self-reference is an inexhaustible source of riddles, paradoxes and surprises. And some theorems, such as those of Gödel. And also “tricks†(in quotes, since they are actually logical games), such as the one that consists of writing something down on a piece of paper and telling the victim: “I have written a statement that may or may not be true. If you say Yes and what I have written is true, you win, if you say NO and what I have written is not true, you also win, otherwise I win. I bet you ten to one that I win.†. And you could equally bet a hundred or a thousand against one, because on the paper it says “You are going to say NO.†.
Grouped elements and schoolgirls on a walk
And if self-reference is an inexhaustible source of surprises and headaches, combinatorics, our other recurring theme of recent weeks, is no less so. As an example, this problem proposed by Ignacio Alonso:
In how many ways can seven elements be grouped into seven groups of three elements, if they are to appear in the same number of groups and two to two only in one group?
The one with the seven elements is reminiscent, in a simplified way, of the classic Kirkman schoolgirl problem, proposed in the 19th century by the English mathematician Thomas P. Kirkman (who made important contributions to combinatorial analysis and group theory) and popularized by Édouard Lucas in one of his compilations of “mathematical recreations†. The one known as the “schoolgirl problem” goes like this:
Fifteen schoolgirls go out for a walk every day of the week, from Monday to Sunday, in an orderly manner, forming five rows of three girls each. How do they have to plan their placement on each and every day of the week so that no pair of schoolgirls share a row for more than one day?
The problem is not simple. I suggest tackling the one with the seven elements first and then moving on, to raise your grade, to the one with the fifteen schoolgirls.
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