How much Malvoisie wine did the Cellarer steal? We got some winners (and others) here!

Click blackboard, gets bigger.

Okay, Brent from Norge/Norway cut through this problem like a red-hot knife through butter. Vleeptron will credit 1 bottle of Malvoisie, or 1 small flask of MD 20/20 (a famous and very inexpensive USA wine), to his account.

On the blackboard above, Brent e-mailed Equations (1) and (2).

The big Sigma Σ notation is a quick shorthand for a sum. (1) implies that d increments by 1 for each new term, so each term is a function of

1...2...3...4...5.......27...28...29...30

Then he tossed in an equation very much like (3), which I used to make XCALC give me the answer at the bottom.

Brent adds:

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Clearly, the solution for D days must approach 100 as D approaches infinity (a nice test to check if the solution is right).

After day 1 (and one pint of wine), 99 pints out of the 100 in the cask is wine. Call this purity 99/100.

On the second day the poor man thus only consumes 99/100 pints, and purity reduces to (99/100)^2. Obviously purity reduces by a factor of 99/100 each day. Remembering that the first day an entire pint was consumed, the answer would be (given I'm not as confused as the Abbot)

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Patthetroll, good on ya for cranking up your Spreadsheet!

Okay, the Puzzle comes from

The Canterbury Puzzles
by Henry Ernest Dudeney

... I got a 1959 Dover reprint, but Dudeney (1847 - 1930) wrote this 4th edition of these puzzles in 1919. No programmable digital computers, no XCALC.

There were mechanical office calculators with a crank, some fancy ones (like for insurance companies) with 12, some with maybe 20 digits. By 1930 they put electric motors in them.

But somehow, in 1912, Dudeney wrote:

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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

....97
73 ---
...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,

[Briggs' table: 1617, the common logs of 1000 numbers, accurate to 14 places]

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 wiley 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 58 decimals deserved severe punishment.

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(I hope I typed that number right.)

Here are the Comments this puzzle generated:

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Bernt Ribbum said...

Pat's answer is obviously wrong... I have mailed the solution to Rob, and he can post it here when he sees it fit :-)
Tuesday, 05 May, 2009

patthetroll said...

Yep, that was massive trolling on my part. Understanding has dawned.. One simple bloody flaw in my logical strain of thought up there in the first comment. Quite a revealing experience when it suddenly dawns on you that you are an utter bloody stupid troll. Someone pass me a very big shovel so I can dig a very deep hole 4 myself. I shall revise may calculations and send them to Bob together with the original source of the puzzle. But I need some coffee and nicotine first to cure the pain and humility and self-loathing. And then find a shovel.
Tuesday, 05 May, 2009

Vleeptron Dude said...

I didn't grok math the first time around either. All my intellectual faculties were in those Youth Days focused entirely on Beauty and a fuzzy sort of Truth, and nothing I was concerned with screamed out for a Scientific Calculator (even though they didn't exist yet).

And now, many years later, please let me assure you that I am not very much far beyond you. If I stop on this picnic table for a smoke, you should catch up with me at any moment.

But here is what I have learned from the math courses I have taken, and the extensive reading I have done in the history of this kind of crap:

THE EXPERIENCE OF LEARNING MATHEMATICS very much resembles being dragged across a hot asphalt parking lot in late July, naked.

Learning this stuff until it makes sense just always, for (almost) everyone, entails Humiliation, Failure, Remorse, Shame, and what's the word for feeling as smart as a garden snail?

In Europe in the late Middle Ages, Aristotelean Logic was taught to every lad at every university.

On the Final Exam, everybody had to answer a question. Most answered it correctly.

But every year, some unfortunate guys would get to their answers via the Pons Asinorum -- the Bridge of Asses.

It is a beautiful bridge made entirely of Wrong Logic. And only Asses can cross this beautiful bridge.

In Real Math College, unless you are Euler or Gauss, you quickly get used to Failing, or getting a real excretory grade like a D+ , and then immediately next semester you take the course again. First, of course, you have to swallow last semester's Humiliation. You'll probably have the same professor.

I *Really* think it was Rilke who said (not in English):

"Everything valuable is difficult."

But it could have been Plato or ABBA.
Tuesday, 05 May, 2009

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Mr P said...

Very interesting post. I'm not sure I understand all of it but I hope to get there.
Tuesday, 05 May, 2009

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Vleeptron Dude said...

Hiya Mr P --

18 months ago I would have made fun of Internet Casino gambling.

Today, comparing all possible available investments -- Internet Casino gambling makes a lot of sense and promises a comparable return to the more traditional financial investments.

Your odds haven't changed. The odds of every other game have.

ANYWAY ...

1. Did you read the Original Problem about the monk stealing wine in the cellar?

2. If you did ... What part of this post don't you understand? Vleeptron always aims to be Clear and Easy to Grok.
Tuesday, 05 May, 2009

Vleeptron Dude said...

3. The story about the Poppies ... well, to people who love the finest cooking, Poppy Seeds are far more precious than that gooey nasty Opium gum in the middle of the flower.

4. XCALC is a freeware desktop calculator with a gazillion functions beyond [+] [-] [*] [/] (and sometimes Square Root}.

5. Reverse Polish Notation / RPN is the way God does arithmetic. The Creator of the Universe uses an HP, not a TI. It was invented by a Polish logician, Lukaciewicz.