Subj:.....A
Puzzling Mixture (S617)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959
With how much water
did the milkman dilute
each of his two cans
of milk?
It is told that an
honest and unsophisticdated milkman
who had boasted much
about his conscientious dealings
and the fact of his
never having disappointed a cust-
omer, found to his
dismay one morning that his supply
of milk was inadequate
to the demands of his patrons.
In fact, his stock
was much too short to serve his route,
and there was no
possiblity of getting more milk.
Realizing the serious
effect this might have on his
buisness, to say
nothing about the disappointment and
inconvenience to
his customers, he was at his wits'
end to know what
to do.
After turning the
matter carefully over in his mind
he decided that he
was too consientous and fair-minded
to show partiality
by serving some and passing others.
He would have to
divide what he had amoung them all,
but would dilute
his milk with a sufficient quantity
of water to make
it meet all demands.
Having found, after
diligent search, a well of exceed-
ingly pure water
which he could conscientiously employ
for the purpose,
he pumped into one of the cans as
many gallons of water
as would enable him to serve all
of his customers.
Having been in the
habit, however, of selling two
qualities of milk,
one for eight cents a quart and the
other for ten, he
proceeded to produce two mixtures,
in the following
ingenious manner.
From Can No. 1, which
contained only water, he poured
enough to double
the contents of Can No. 2, containing
the milk. Then
from No. 2 he poured back into No. 1
just as much of the
mixture as he had left water in
No. 1. Then,
to secure the desired proportions, he
proceeded to pour
back from No. 1 again just a suffi-
cient quantity to
double the contents of No. 2. This
left an equal number
of gallons in each can, as may be
readily shown, although
there were two gallons more of
water than milk in
can No. 2.
Now, this is not
as complicated as it looks, for it
requires but three
changes to equalize the contents of
the two cans.
Can you determine exactly how much milk
and water each can
finally contained? |
.
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