Subj:.....The
Merchant Of Bagdad (S629)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959
Show
how the merchant measured the wine and water.
A merchant of Bagdad
who catered to the wants of pilgrams
who crossed the desert,
was once confronted by the following
perplexing problem.
He was visited by the leader of a caravan,
who desired to purchase
a store of wine and water. Presenting
three ten-gallon
vessels, he asked that three gallons of wine
be put in the first,
three gallons of water in the second, and
three of wine and
three of water mixed in the third, and three
gallons of water
be given to each of his thirteen camels.
As water and wine,
according to Oriental usage, are sold only
in quantities of
even number of gallons, the merchant had only
a two and a four
gallon measure wherewith to perform a feat
which presents some
unexpected difficulties. Nevertheless,
without resorting
to any tricks or device, or expedient not
used in measuring
problems of this type, he dispensed the water
from a full hogshead
(63 gallons), and the wine from a full
barrel (31½
gallons), in the required proportions, without any
waste whatever.
In how few manipulations can the feat be
performed, counting
every time liquid is drawn from one
receptacle to another
as a manipulation?
.
.
|
 |
Finger pointing down
from darrell94590 on 1/2/2006 |
.
...
THE SOLUTION
The number at the
end of each paragraph denotes the number of
manipulationd in
that paragraph.
The hhd. contains
63 gall. of water and the barrel 31½ gall. wine.
Fill the three 10-gall.
bottles with wine, pouring remaining 1½
gall. into 2-gall.
measure, thus empting barrel (4 manipulations).
By means of the 4-gall.
measure fill barrel from hhd., eventually
leaving ½
gall. in 4-gall. measure. Give this ½ gall. to camel
No. 1. By means
of 4-gall. measure return 28 gall. of water from
barrel to hhd.
Pour 1½ gall. wine from 2-gall. measure into 4-gall.
measure. Pour
2 gall. water from barrel into 2-gall. measure and
return to hhd.
Draw off remaining 1½ gall. water from barrel into
2-gall. measure and
give this to camel No. 2. Pour 1½ gall. wine
from 4-gall. measure
into 2-gall. measure (37 manipulations).
Repeat the whole of
the operations in the last paragraph eleven
more times, so that
six camels shall have each received two ½ gall.
drinks, and another
six camels two 1½ gall. drinks. But on the
tenth and eleventh
repetition, instead of returning the 2 gall. to
hhd., deliver them
to any two camels who have already received two
½ gall. only.
Eight camels have now received 3 gall. each, and
four camels 1 gall.
each, and there is 35 gall. of water in hhd.
(407 manipulations).
Fill barrel from hogshead,
using 4-gall. measure and give ½ gall.
over to camel No.
13. Draw 3 gall. from hogshead into 4-gall.
measure (18 manipulations).
Return all wine to
hogshead. Empty barred into three 10-gall.
bottles, and draw
remaining 1½ gall. into 2-gall. measure. Return
contents of three
bottles to barrel, pour 1½ gall. from 2-gall.
measure into bottle
No. 1 (12 manipulations).
Fill the 2-gall. measure
from 4-gall., leaving 1 gall. in 4-gall.
Fill barrel from
2-gall. measure, and give remaining ½ gall. to
camel No. 13.
Give five camels 2 gall. each, all the camels
have now been served
(13 manipulations).
Fill the two empty
bottles from barrel, and draw remaining 1½
gall. into bottle
No. 1. Return contents of bottles Nos 2 and
3 to barrel (5 manipulations).
Pour 1 gall. from
4-gall. measure into No. 2 bottle. Put 6 gall.
wine in bottle No.
3, using 2-gall. and 4-gall. measures. Empty
the 1 gall. from
No. 2 into 4-gall. measure and fill up that
measure with wine
from bottle No. 3. Pour contents of 4-gall.
measure into bottle
No. 2. Draw 2 gall. water from barrel and
put into bottle No.
2 (10 manipulations).
The thirteen camels
have now each received 3 gall. of water, one
of the 10-gall. bottles
contains 3 gall. of water, another 3 gall.
of wine, and the
third 3 gall. of wine and 3 gall. of water mixed.
The hogshead contains
25½ gall. of wine, and the barrel 18 gall.
of water. Total
number of manipulations: 506.
[In an interview published
in The Strand magazine, April 1926,
Henry Dudeney, England's
great puzzlist, disclosed that Loyd once
appealed to him for
help on this problem. Loyd had offered cash
prizes to his readers
for the best solution and was anxious to
avoid giving them
by having an answer of his own that topped all
those received.
Dudeney worked out a solution in 521 moves
which he later reduced
to the 506 given above. This did the
trick and Loyd always
claimed that Dudeney had saved him
thousands of dollars.
-- M.G.] |
