The Locomotive - Lighthouse Survival Blog

1893] THE LOCOMOTIVE. 79
1. A man liad five iticccs of j^old cliaiii, each piece consisting of tlirce links.
Wishing to have tlicni united into u single chain of lo links, he took them to a jeweler,
who made him two propositions. He would do the work for S.! cents, or he would
charge 10 cents for each link he had to cut. Whicli was the l)ett(r otTir ''.
3. Two numljers were jnultiplied together, hut when the e.\a»uj)le was done, the
multiplier and multiplicand were accidentally rubbed out. The rest of the example
was as follows:
TCTT
5971
1706
237087
What were the two numbers that were multiplied together, and which of them was the
multiplier ?
3. A man bought some pigs, some cows, and some hens. He paid 20 cents for
each hen, $4 for each pig, and $20 for each cow. He bought 100 creatures in all, and
they cost him just $400. How many of each did he buy ?
4. If we admit that there are more cows in the world than there are hairs in any-
one cow's tail, does it follow that there are at least two cows in the world with the
same number of hairs in their tails ? (All " catches,'' such as bald-tailed cows and cows
without tails, are barred out.)
5. Four men play whist. A holds the ace of clubs, the queen, seven and three of
spades, and the king, queen, and- seven of diamonds. B holds the jack and king of
spades, the ten and deuce of diamonds, and the nine, eight, and seven of clubs. C
holds the king and cjueen of hearts, the king, ten, and six of clubs, and the nine and
three of diamonds. D holds the ace, ten, and nine of spades, the five of hearts, and the
eight, six, and four of diamonds. Every man is supposed to know what every other
man holds. Hearts are trumps, and A is to lead. It is required to prove that
A and C can win every trick, no matter how B and D may play (provided they follow
suit). This is an excellent problem, and it seems impossible until the underlying prin-
ciple is perceived. There are no catches to it, and B and D do their utmost to take a
trick.
6. There is an army, 25 miles long, which is marching forward at a uniform rate.
At a certain instant a courier leaves the rear of the army, travels to the front and delivers
his message, and returns to the rear again without stopping. He travels at a uniform
si')eed, and when he gets to the rear end again he finds that the rear of the army is
where the front end was when he started. How far did he travel ? (This problem is
best solved by algebra, and is a very good one.)
7. If three dogs catch three rats in three minutes, how many dogs (at the same
rate) will it take to catch 100 rats in 100 minutes ?
8. A man had a rock weighing forty pounds. It fell and broke into four pieces,
and he discovered that by using these pieces as weights he could weigh any whole
number of pounds from 1 up to 40. What did each piece weigh ?
9. Mr. Brown had eight gallons of cider, in an eight-gallon measure, and wished
to give four gallons of it to Mr. Smith. Mr. Smith had only two measures, one holdingthree
gallons, and one holding five. How could the cider be divided equally by using
only these three measures ?
10. There are two spheres of metal, each four inches in diameter, and plated on
the outside with copper, so that they look exactly alike. It is known that one is made
of lead, and the other of aluminium; but the lead one is hollow, so that it weighs just
the same as the other one. How can we find out which is which, without injuring them
in any way ?
11. What would happen if an irresistible force should be exerted on an immovable
body ?