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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?

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 Finger pointing down from darrell94590 on 1/2/2006
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 Drawing from Ripleys-Believe It Or Not
...

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.]

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