Il giardino di Tolstoy
A.V. Tsinger, a prominent physicist, recalls Lev Tolstoy posing the following problem, one that the great writer like very much.
A team of haymakers were assigned the task of scything two meadows, one twice the size of the other. Half a day the team worked on the larger meadow. Then it split into two equal groups: the first remained in the larger meadow and finished it by evening; the second group scythed the smaller meadow, but by evening there still remained a portion to do; this portion was scythed the next day by one haymaker in a single day's work. How many men were there in the team?
...
Professor A. V. Tsinger sent me a detailed and extremely interesting account of the background of this problem, in his opinion, is that "it is non in the least an algebraic problem, but an arithmetic one and what is more it is very simple, the only difficulty being its unusual form."
Professor Tsinger goes on to describe how the problem originated. "in the period when my father and my uncle I.I. Raevsky ( a close friend of L. Tolstoy) studied at the mathematics department of Moscow university, there was a subject something like pedagogy. It consisted of students visiting an ordinary city school selected by the University to acquire some teaching experience under the guidance of the best teachers. Now there was a student by the name Petrov, a friend of Tsinger and Raevsky, and he was extremely gifted and imaginative fellow. This Petrov (who died at a very early age of tuberculosis, I believe) maintained that the children were spoiled at arithmetic lessons by a standard problems and routine methods of solving them. To confirm his believe, Petrov invented problems that were quite out of the ordinary and put the best teachers in a quandary, but were easily solved by capable pupils who had not yet spoiled by school. One of these was the problem of the team of scythemen (Petrov thought up a number of such problems). Experienced teachers were able, quite naturally, to solve them with the aid of equations, but a simple arithmetic solution eluded them. Yet, the problem is so simple that there is no need to resort to algebraic methods.
"If ...<<omissis>>..., then there must be <<omissis>> workers.
"Tolstoy, who all his life enjoyed tricky problems that were not too involved, learned about this problem from my father when still a young man. When I meet Tolstoy -already an old man- and discussed the problem with him, he was most delighted by the fact that the problem becomes still clearer, literally transparent, if a very simple drawing is employed in the solution".
problema proposto da From: Rocco Lupoi
"Una squadra di trebbiatori avevano il compito di lavorare su due campi, uno il dopo dell'altro. La squadra lavorò per metà giornata sul campo più grande. Poi la squadra si divise in due gruppi: il primo rimase nel campo più grande e terminò il lavoro per la sera. Il secondo gruppo lavorò sul campo più piccolo, di cui a sera rimase una parte ancora da finire, che fu terminata il giorno dopo da un solo trebbiatore che lavorò tutto il giorno. Quanti uomini c'erano nella squadra?"
traduzione a cura di: Stefano Machera
soluzione
La soluzione è contenuta in un Foglio di Lavoro di Microsoft Excel
soluzione proposta da: Stefano Machera