SOLUTIONS
44.—
The Riddle of the Sack Wine.
The question was—Did Brother Benjamin take more wine from
the bottle than water from the jug ? Or did he take more water
from the jug than wine from the bottle ? He did neither. The
same quantity of wine was transferred from the bottle as water was
taken from the jug. Let us assume that the glass would hold a
quarter of a pint. There was a pint of wine in the bottle and a
pint of water in the jug. After the first manipulation the bottle
contains three-quarters of a pint of wine, and the jug one pint of
water mixed with a quarter of a pint of wine. Now, the second
transaction consists in taking away a fifth of the contents of the jug,
that is one-fifth of a pint of water mixed with one-fifth of a quarter
of a pint of wine. We thus leave behind in the jug four-fifths of a
quarter of a pint of wine, that is one-fifth of a pint, while we transfer
from the jug to the bottle an equal quantity (one-fifth of a pint)
of water.
45.—The Riddle of the Cellarer.
There were 100 pints of wine in the cask, and on thirty occasions
John the Cellarer had stolen a pint and replaced it with a pint of
water. After the first theft the wine left in the cask would be
99 pints ; after the second theft the wine in the cask would be
9
fW- pints (the square of 99 divided by 100) ; after the third theft
there would remain
9
r'oc^o
9
(the cube of 99 divided by the square of
100) ; after the fourth theft there would remain the fourth power
of 99 divided by the cube of 100; and after the thirtieth theft,
there would remain in the cask the thirtieth power of 99 divided by
the twenty-ninth power of 100. This by the ordinary method of
calculation gives us a number composed of 59 figures to be divided
by a number composed of 58 figures ! But by the use of logarithms
it may be quickly ascertained that the required quantity is very nearly
73i
9
o% pints of wine left in the cask. Consequently the cellarer stole
nearly 26*03 pints. The monks doubtless omitted the answer for
the reason that they had no tables of logarithms, and did not care to
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