Mathematical_Recreations-Kraitchik-2e

40 Mathematical Recreations
without bothering to set it, and I noted the exact moment A
of my departure according to its reading. At my friend's
house I noted the exact times, hand k, of my arrival and departure
by his clock. On returning I noted the time B of my
arrival according to my clock. The length of my absence
was B - A. Of that time k - h minutes were spent with my
friend, so the time spent in traveling, t in each direction, was
2t = (B - A) - (k - h). Thus the correct time when I
reached home was k + t.
50. I am going hunting and wish to take my gun with me
on the train. The ticket agent tells me I may not take it in
the coach, while the baggage man will not take it because of
its excessive length (1.7 yards), since he is forbidden to accept
for shipment any article whose greatest dimension exceeds 1
yard. What should I do?
Answer: Pack it diagonally in a cubic case 1 yard on a
side. The length of the diagonal is v'3 = 1.73+ yards.
51. A large furniture store sells 6 kinds of dining-room
suites, whose prices are $231, $273, $429, $600.60, $1,001, and
$1,501.50, respectively. Once a South American buyer came,
purchased some of each kind of suite, paid the total amount
due, $13,519.90, and sailed for South America. The manager
lost the duplicate bill of sale and had no other memorandum
of each kind of suite purchased. Can you help him fill the
order correctly? (Tarry)
Solution: Let x, y, z, t, u, v be the respective numbers of
each kind of suite purchased. Then 2,31Ox + 2,730y +
4,290z + 6,006t + 10,0l0u + 15,015v = 135,199. This equation
can be solved most readily by congruences. With reference
to the moduli m, we must have
9x == 12.
2y = 9
6z == 1
(m = 13),
(m = 11),
(m = 7),
x == 10.
y == 10.
z == 6.