A merchant was going to market carrying in his cart twelve big clay jars filled with vegetable oil.

logic/oil.jars New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A merchant was going to market carrying in his cart twelve big clay
jars filled with vegetable oil.  It started raining heavily, and the
roads became impassable, so he turned into the nearest farm and asked
the peasant to keep the jars for him.  In a fortnight the merchant was
back, but as he was reloading the jars from the cellar to his cart, he
opened them, and it was discovered that 6 jars were only half full.
"Oh you swindler," shouted the merchant, "you have stolen my oil!"
"Swindler yourself," the peasant replied, "they were half full when you
gave them to me!"  Can you find a way to find out which of the two was
lying?

Show solution

[ Editor: posted by Chris Cole for olimpus@dol.ru, March 1998.  The
intended answer is not in the collected postings; two replies follow. ]

Well...  This is probably not what you're looking for, but seems a
reasonable direction to me:

The jars were closed when the peasant got them, and closed when the
merchant returned.  There is no reason for the peasant to have opened
the jars.  Therefore, if the peasant has opened the jars, which he
would have had to do in order to know that they were only half full,
then something's clearly amiss, and the peasant is not to be trusted.
Thus, one can be more inclined to trust the merchant in this case.

(I know, that's not a definite answer, but I like it.  :-)

-- Snibor Eoj <jmrobins@sccs.swarthmore.edu>

Given that the jugs were clay -- which should be a little porous, even
if glazed (if the jugs were only for carrying oil, they probably
wouldn't be glazed; the merchant's reluctance to venture far in the
rain also attests to his worries about water damage) -- the vegetable
oil might have had a chance to soak in during the trip.  Then, all one
would have to do to test the peasant's story is put a drop of water
above the halfway mark in the jug; if it soaked in, the story was true,
if it beaded (oil being hydrophobic), the peasant must have stolen some
of the oil.  (To fend off questions of what counts as "soaking in" and
what counts as "beading", you could have a 'control droplet' at the top
of the jug.)

-- Simon DeDeo <sdedeo@fas.harvard.edu>