Mathematical_Recreations-Kraitchik-2e

fl6
Mathematical Recreations
half a day. Tell me in what a short time we should fill
it, pouring water from wings, bow, and jar all at once.
(xiv: 135)
Answer: n of a day.
19. A: "Give me ten minae and I become three times as
much as you." B: "And if I get the same from you I am five
times as much as you." How much each are A and B? (xiv:
145) Answer: 15t and 18+.
20. A: "Give me two minae and I become twice as much
as you." B: "And if I got the same from you I am four times
as much as you." How much each are A and B? (xiv: 146)
Answer: 3t and 4t.
The next problem has a rather interesting origin. In the
Middle Ages it was quite common for teams to compete in
the solution of problems. These competitions were something
like the sporting events of our time. The competitors
were informed beforehand of the questions to be asked. A
famous match of this sort was in 1225 when the team backed
by the Emperor Frederick II opposed Leonardo of Pisa (better
known as Fibonacci, that is, filius Bonaccii). The latter
was the au thor of "Liber Abaci" (1202), probably the first
book in Europe to teach the use of the decimal system. "Liber
Abaci" had a wide circulation, and for more than two
centuries was a standard authority and a source of inspiration
for numerous writers. Fibonacci's reputation was so
great that the Emperor Frederick II stopped at Pisa in 1225
in order to hold this mathematical tournament to test Leonardo's
skill, of which he had heard such marvelous accounts.
The team of Frederick II consisted of John of Palermo and
Theodore. One of the questions posed to Fibonacci was the
following:
21. Find a perfect square which remains a perfect square
when increased or decreased by 5.