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  1. #1
    New Lounger Joey's Avatar
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    Pennies On A Chessboard

    Without using a calculator (using old fashioned pencil and paper) and without cheating (by looking in the internet or a book for the answer):

    If you put one penny on the first square of a chessboard, two pennies on the second, four pennies on the third and so on (doubling the amount of pennies for each square), until the last square (64th square), what would the total amount of pennies be? What would the total dollar amount be?

    Hint: You'd be richer than Bill Gates. In fact, you'd be the richest man ever in history.

  2. #2
    5 Star Lounger
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    It's the sum of the powers of 2 from 0 through and including 63.

    In a related or slightly unrelated question, who is/was the richest individual in history?

    This is quite debatable based on history, currency conversion, what you can buy where you live(d), etc.
    Economist Branko Milanovic wrote about this in "The Haves and The Have-Nots: A Brief History of Global Inequality."

    He concluded that in order to compare wealth and income in historical periods, each candidate should be situated in their historical context and measure their economic power in terms of their ability to purchase human labor (of average skill) at that time and place. [interesting concept, says I]

    An example: The Roman politician Marcus Crassus was thought to have been worth 200 million sesterces. Given his apparent wealth of 200 million sesterces, his annual income, at a 6% interest rate was roughly 12 million sesterces. The average annual income of a Roman at that time was roughly 380 sesterces, so Crassus' income equaled 32,000 Romans.

    Now figure out Bill Gates, J.D. Rockefeller, Carlos Slim, etc. Hmmm.

    Last edited by kweaver; 2014-06-23 at 02:43.

  3. #3
    Bronze Lounger Maudibe's Avatar
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    A prime example of why there is an upper limit on gaming tables in a casino, to prevent progressive betting. While you are speaking of wealth, what is the most expensive and precious thing ever?

  4. #4
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    Quote Originally Posted by Maudibe View Post
    A prime example of why there is an upper limit on gaming tables in a casino, to prevent progressive betting. While you are speaking of wealth, what is the most expensive and precious thing ever?
    Wholly depends on definition of "thing," and "expensive" and "precious."
    Is a city or state or country a thing? Is a river a thing? Is the Earth a thing?
    Is "expensive" only the price asked for something? Or is it the amount actually paid? (One can ask far more than anyone will pay, but does that actually affect the value?) What is "precious"? Is a human life more precious than anything else? Everyday experience would tell us "NO".

    A valid answer would have to take all this, and more, into account....

    And by the way, I don't think the table limits in Vegas are for the protection of the house, they are for the protection of the players. Any real high roller who wants higher limits needs only to whisper it to the pit boss and he/she will be shown to a private room.
    Last edited by cosmlou; 2014-06-24 at 00:37. Reason: Another thought...

  5. #5
    5 Star Lounger
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    When I fill up at the gas pump in southern CA, I usually think this is the most expensive LIQUID.
    But, alas, I remember reading some time ago that liquids like King Cobra Venom (by the gallon) was very expensive (not sure who wants this or why).
    Also, Chanel #5 was also rumored to be expensive (by the gallon).

    I think my ink cartridges for my printer are more expensive by the gallon than even SoCal gas! YIKES. Of course, that explains why the printer itself is inexpensive.

  6. #6
    Bronze Lounger Maudibe's Avatar
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    Another hint is that even though it is the most priceless thing, one cannot have it for a long period of time.

    Kw,

    If I am not mistaken many colognes have snake venom as an ingredient. I must have been wealthy for a period of time when my first girlfriend gave me two gallons of her venom.

    Cosmlou

    In my question a "thing" refers to a materialistic object of value that is attainable but no amount of money can buy it. Can someone own a planet? No. Can someone own a city? Yes, but what I am thinking is much more valuable. I think you are reading too much into it.

    BTW, casinos care little about the protection of the players. If you understand progressive betting, you will know that the upper limit does protect the casino's interest. Without an upper limit, a players probability of having a winning night rapidly approaches 100% with enough cash in hand. Raising and returning of the upper limit is at the discretion of the Pit Boss. But if you use progressive betting, you have a better chance of getting thrown out of the casino than being awarded higher stakes.

  7. #7
    Bronze Lounger Maudibe's Avatar
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    In an answer to the original question, greater than 92 quadrillion dollars.

  8. #8
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    1+2+4+...+2^63=2^64-1
    18.4x10^18

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