¿In how many different ways can Tibetan monks combine the letters of their alphabet in their search for the true name of God??
CARLO FRABETTI
19 MAY 2017
If the nine muses have to go out for a walk three by three without any of them repeating companions or failing to go out with any, as we saw last week, each muse comes out four times, since on each occasion she goes with two of her eight companions. will have occurred, well, 9 x 4 = 36 individual walks, and as in every walk three muses participate, the number of walks will be 36/3 = 12. If we number the muses of 1 al 9, the walks of the first could be 123, 145, 167 and 189; those of the second, without repeating any of the previous couples, 246, 258 and 279; those of the third, 349, 357 and 368; those of the fourth and fifth, 478 and 569, and there are no more possibilities without any couple repeating. Obviously, the solution is not unique. On your first walk, the first muse could have dated any of the 28 pairs that can be formed with the remaining eight, and from there things continue to branch out until giving… ¿how many different solutions?
This problem is a simplified version of the famous “schoolgirl problem.”” proposed by the British mathematician Thomas Kirkman in 1851, that says like this:
Fifteen schoolgirls go out in rows of three for seven days in a row. ¿How are they to form each day so that at the end of the week there have not been two of them that have gone in the same line more than once?
Variations with limitations
Combinatorial problems in which some condition limits the number of possible combinations (or variations, or permutations), like the ones we just saw, They tend to be especially interesting, and often more complex than they appear at first glance.
One of the most famous is of literary origin: in his story The nine billion names of God, Arthur Clarke tells the story of some Tibetan monks who constantly combine the letters of their alphabet to try to form the true name of God. Taking into account that the Tibetan alphabet consists of thirty letters, that the name of God cannot have more than nine letters and that the same letter cannot appear more than three times in a row (This would result in a name that would be unpronounceable even for a Tibetan monk.), ¿The number of possible divine names is actually on the order of billions.? ¿Or those who mistakenly translate billions as trillions are closer to the truth in this case.?
Carlo Frabetti He is a writer and mathematician, member of the New York Academy of Sciences. He has published more than 50 popular science works for adults, children and young people, among them damn physics, Damn math o the big game. He was a scriptwriter for The crystal ball.
