Dionysus the Scyllun

Of the two problems of desert crossings raised last week (and mentioned in the previous week), the first and most difficult provoked a debate that was not even extinguished when the "official" solution was published (see comments from Brossaist balance, sobtes everything from no. 130). As for the second, at the time of writing these lines still follows the debate, so, true to the slogan of not ditching the discussions of readers, I will not give a definitive answer (if any, since the statement lends itself to different interpretations: see comments from last week).

And since there are no two without three, here's a third problem of the same type:

Five men try to cross a desert, and each one carries supplies for five days. After traveling a certain distance, one of the men becomes ill and has to return, with enough supplies to get to the starting point. Another day the same thing happens to a second man, and then to a third man and then to a room,

How many days could the fifth man do in the desert before returning to the starting point?

It is assumed that the journey takes place in days of a whole day, and that men can give supplies to each other,

A new decade?

The year we have just entered is leap, since 2020 is divisible by 4 but not by 400; otherwise the number 2020 does not have very noticeable characteristics. It is of the way abab, and, as we saw in its day, the numbers of the form abcabc, like 734.734, do have a curious property (what is it?), which lends itself even to perform ingesting a well-known divinatory "mathematical" trick. Do the numbers of the form abab any property comparable to that of their older brothers abcabc?

But there is an extra-mathematical question (or perhaps not so much) that makes the year 2020 special. It is common to speak in news and magazines at the beginning of a new decade these days; but does a new decade really start on January 1, 2020? The controversy is similar (though not identical) to that raised in 2000 with respect to the turn of the century (and the millennium). Did the 21st century (and the third millennium) begin on 1 January 2000, as some media 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 Dionysus the Munal and the equivocal concept of "year zero". My shrewd readers can't stop participating in this debate. And, in any case, happy year and happy decade, whether or not it has already begun,