Our Indian from last week had little chance of getting out unscathed. To do this, the three cowboys who shot him had to miss at the same time; the probability that the first one fails is 1/6, that of the second 1/2 and that of the third 5/6, so the probability that they all fail is 1/6 x 1/2 x 5/6 = 5 / 72, less than 7%. The symmetry of the situation (the hit rate of the first is the same as the miss rate of the third) makes the probability that all three gunmen hit at the same time is the same as that of all miss.
And speaking of probabilities and numerical symmetries, what is the probability that a (landline) telephone number in Barcelona is capicúa? And what about a Girona phone number?
In the 21-card trick, the chosen card will be the fourth from the central pile the third time we arrange them in three piles, that is, the one that has remained in the center of the deck after successive rearrangements of the piles. A classic of easy execution, but very effective. The demo is simple, but long and cumbersome.
The remote edge
Last week’s rider on the run led me to think of a memorable flight forward from literature: that of the protagonist of The seven messengers, one of the most famous stories by Dino Buzzati.
A prince leaves with his entourage to explore the confines of his kingdom, which seem unreachable. Seven messengers on horseback keep him in contact with the capital; but, logically, as the expedition moves away, the messengers take more and more time on their round trip:
“Not used to being far from home, I sent the first messenger, Alejandro, the night of the second day of travel, when we had already traveled some eighty leagues. To ensure continuity of communications, the next night I sent the second, then the third , then to the fourth, and so on until the eighth night of the trip, when Gregorio left, the first had not yet returned.
“This reached us on the tenth night, while we were planting our camp to spend the night in an uninhabited valley. I learned from Alejandro that his speed had been less than expected; I had thought that, riding alone and riding a magnificent steed, he could travel twice as far as us in the same time; however, he had only been able to walk the equivalent of one and a half times; in a day, while we advanced forty leagues, he traveled sixty, but no more ”.
The seven messengers – A, B, C, D, E, F and G. according to the initials of their names – are supposed to always travel at the same speed, and so does the prince’s expedition. So that:
“Bartolomé, who left for the city on the third night of his journey, returned on the fifteenth. Gaius, who left the fourth, did not return until the twentieth. I soon realized that it was enough to multiply the days used so far by five to know when the courier would reach us ”.
Is the traveling prince’s conclusion correct?
In Buzzati’s haunting tale, the prince grows old without reaching his goal; but nothing prevents us from imagining a less frustrating ending:
If the confines of the immense kingdom were 1,000 leagues from the capital, which of the seven messengers would bring the good news to court that the expedition had achieved its objective?
Carlo Frabetti 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, including ‘Damn physics’, ‘Damn mathematics’ or ‘The great game’. He was a screenwriter for ‘La bola de cristal’.