Answers 267It was not stated that the sons were to receive those fractions of seventeen.
The proportions are thus o/1s, o/1S, and ¥is, so if the sons receive respectively
9, 6, and 2 horses each, the terms of the legacy will be exactly carried
out. Therefore, the ridiculous old method described does happen to give
a correct solution.
A correspondent suggested to me the ingenious solution:
~, i.e., 2 and lover = 3
Y.!, i.e., 3 and lover = 4
~, i.e., 9 and lover = 10
17- EQUAL PERIMETERS
The six right-angled triangles having each the same, and the smallest pos-
sible, perimeter (720), are the following: 180, 240, 300; 120, 288, 312; 144,
270, 306; 72, 320, 328; 45, 336, 339; 80, 315, 325.
174. COUNTING THE WOUNDED
The three fractions are respectively 4%0, 4~;o, and 4%0. Add together 40, 45,
and 48, and deduct twice 60. The result is 13, as the minimum number
for every 60 patients. Therefore as the minimum (who could have each lost
an eye, an arm, and a leg) was 26, the number of patients must have been 120.
- A COW'S PROGENY
Note the following series of numbers, first considered by Leonardo Fibonacci
(born at Pisa in 1175), who practically introduced into Christian Europe our
Arabic numerals:
0, 1, 1,2,3,5, 8, 13,21,34, ... , 46,368.
Each successive number is the sum of the two preceding it. The sum of
all numbers from the beginning will always equal 1 less than the next but one
term. Twice any term, added to the preceding term, equals the next but one
term. Now, there would be 0 calf in the first year, 1 in the second, 1 in
the third, 2 in the fourth, and so on, as in the series. The twenty-fifth term is