Math Puzzle - The Riddle Of The Cellarer

The Riddle Of The Cellarer

Then Abbot David looked grave, and said that this incident brought to his mind the painful fact that John the Cellarer had been caught robbing the cask of best Malvoisie that was reserved for special occasions. He ordered him to be brought in.

"Now, varlet," said the Abbot, as the ruddy-faced Cellarer came before him, "thou knowest that thou wast taken this morning in the act of stealing good wine that was forbidden thee. What hast thou to say for thyself?"

"Prithee, my Lord Abbot, forgive me!" he cried, falling on his knees. "Of a truth, the Evil One did come and tempt me, and the cask was so handy, and the wine was so good withal, and—and I had drunk of it ofttimes without being found out, and—"

"Rascal! that but maketh thy fault the worse! How much wine hast thou taken?"

"Alack-a-day! There were a hundred pints in the cask at the start, and I have taken me a pint every day this month of June—it being to-day the thirtieth thereof—and if my Lord Abbot can tell me to a nicety how much good wine I have taken in all, let him punish me as he will."

"Why, knave, that is thirty pints."

"Nay, nay; for each time I drew a pint out of the cask, I put in a pint of water in its stead!"

It is a curious fact that this is the only riddle in the old record that is not accompanied by its solution. Is it possible that it proved too hard a nut for the monks? There is merely the note, "John suffered no punishment for his sad fault."

Answer:

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 9801/100 pints (the square of 99 divided by 100); after the third theft there would remain 970299/10000 (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 73-97/100 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 face the task of making that long and tedious calculation in order to get the quantity "to a nicety," as the wily cellarer had stipulated.

By a simplified process of calculation, I have ascertained that the exact quantity of wine stolen would be

26.0299626611719577269984907683285057747323737647323555652999

pints. A man who would involve the monastery in a fraction of fifty-eight decimals deserved severe punishment.

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The Riddle Of The Cellarer

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