Of the two desert crossing problems raised last week (and already mentioned in the previous one), the first and most difficult provoked a debate that did not end even when the “official” solution was published (see comments from Balancing rubbish, especially from No. 130). As for the second, at the time of writing these lines the debate is still going on, so, faithful to the slogan of not settling the discussions of the readers, I will not give a definitive answer (if there is one, since the statement lends itself to different interpretations: see comments from last week).
And since there are not two without three, here is a third problem of the same type:
Five men attempt to cross a desert, each carrying five days’ worth of supplies. After traveling some distance, one of the men falls ill and has to return, with enough provisions to reach the starting point. Another day the same thing happens to a second man, and then to a third and then to a fourth.
How many journeys could the fifth man make in the desert before returning to the starting point?
The crossing is supposed to be done in full day’s journeys, and the men can give provisions to one another.
A new decade?
The year we just entered is a leap year, since 2020 is divisible by 4 but not by 400; for the rest, the number 2020 does not present very remarkable characteristics. Or if? It is of the form abab, and, as we saw in its day, numbers of the form abcabc, such as 734,734, do have a curious property (what is it?), which even lends itself to performing a well-known “mathmagic” trick. divinatory. Do numbers of the form abab have any properties comparable to their older brothers abcabc?
But there is an extra-mathematical question (or maybe not so much) that makes the year 2020 special. It is common that, these days, news and magazines talk about the beginning of a new decade; but does a new decade really start on January 1, 2020? The controversy is similar (although not identical) to the one raised in 2000 regarding the turn of the century (and millennium). Did the 21st century (and the third millennium) begin on January 1, 2000, as some media outlets claimed? Or did the 21st century begin in 2001? A controversy that refers to the updating of the Christian calendar undertaken in the 5th century by Dionysius the Meager and the misleading concept of “year zero”. My astute readers can not help but participate in this debate. And, in any case, happy new year and happy decade, whether it has already started or not yet.
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 mathO The big game. He was a screenwriter for The Cristal ball