September 26, 2020

Problematic flights | Science | THE COUNTRY

In a drawer with 15 brown socks and six black socks, the probability of getting two at random is both brown is, as we saw last week, 15/21 x 14/20 = 1/2. If we are satisfied that they are both of the same color, it also serves that they are both black, whose probability is 6/21 x 5/20 = 1/14, so the probability goes from 1/2 to 1/2 + 1 / 14 = 4/7.

The problems of objects (balls, coins, candies, socks …) taken at random from one or several boxes constitute a very numerous and interesting "family" within the logical-mathematical riddles, and in previous deliveries of The game of logic We have seen a few. The most elementary is surely the classic of the drawer with six brown and six black socks. How many do we have to take out, at least, to be certain that there are two of the same color? And to have the certainty that there will be two blacks? It is very simple, but it can be complicated at will by adding socks, drawers and conditions. For example:

There are three drawers, one with only black socks, another with only brown socks and another with half black and half brown. We put our hands in a random box and took out a black sock. What is the probability that, if we remove another sock from the same drawer, it is also black? Does this probability depend on the total number of socks? What if there is not half and half in the mixed drawer, but a black sock and nine brown ones?

Atypical flights

The allusion to a hypothetical flying horse as the mythical Pegasus gave rise to a wide debate on the possibility of such a portent and on the very concept of flight (see comments of last week), which is a good excuse to raise some related riddles with the theme

If on the Moon there was an area with an atmosphere similar to the terrestrial one (for example, contained under a huge dome), could a winged horse similar to Pegasus fly there?

The fearsome pirate Long John Silver sets out to cross a precarious wooden bridge that only holds a maximum of 80 kilos, which is exactly what he weighs; but after a few steps the bridge begins to creak alarmingly, and the pirate remembers too late that his parrot, perched on his shoulder, weighs a kilo, thus exceeding the safety limit. The bird also realizes the danger and soars the flight. What happens next? What else could the parrot have done to avoid the catastrophe?

With a constant wind in favor, a pterodactyl takes 4 hours on the outward journey, and on the return trip, with the same wind against it, it takes 5 hours. What can we deduce from these data?

Carlo Frabetti He is a writer and mathematician, a member of the New York Academy of Sciences. He has published more than 50 scientific dissemination works for adults, children and young people, among them Damn physics, Damn mathematics or The big game. He was a screenwriter The Cristal ball.