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  1. #1
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    The Leprechaun's Challenge

    While pulling up a piece of blackthorn root that you think would make a fine shillelagh, a glimmer of light from below the trunk catches your eye. As you investigate further, you find that there is a hidden hollow beneath the tree. Inside the hollow you find five variously sized chests each filled with gold coins. Suddenly a tiny red-bearded man dressed in green appears. “Ahh! You’ve come to steal my treasure!” He shouts. “You must think yourself pretty clever to have found my hidey-hole. Not so clever I’ll wager.” The little man snaps his fingers and suddenly a weighing scale appears at your feet. “Every genuine gold coin in this trove weighs precisely one ounce. But not all that glitters is gold, my friend,” he says with a smirk. “A false coin weighs exactly one hundredth of an ounce more or less than a true coin. All the coins in any single chest are identical. This scale will give you an accurate and precise reading. You may weigh whatever coins you like, but you may take only one reading from the scale. If you can correctly tell me the nature of coin in each chest, I’ll reward you with a bag of gold. Otherwise, I’ll put a curse on you.


    What strategy can you use to pass the leprechaun’s challenge and leave with a bag of gold?

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  3. #2
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    Re: The Leprechaun's Challenge

    Just some musings....

    You can't take one coin from each chest and then weigh a subset of them, because you won't know anything about the chests of the coins that you didn't weigh, and you won't know how any +/- 0.01 oz are distributed amongst the coins you did weigh.

    Any winning strategy will have to be agnostic WRT the number of authentic coins, since it's impossible to tell from one scale reading whether you had false coins whose errors cancelled or whether you have authentic coins.
    If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard
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  4. #3
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    Re: The Leprechaun's Challenge

    Quote Originally Posted by CliveStaples View Post
    Just some musings....

    You can't take one coin from each chest and then weigh a subset of them, because you won't know anything about the chests of the coins that you didn't weigh, and you won't know how any +/- 0.01 oz are distributed amongst the coins you did weigh.

    Any winning strategy will have to be agnostic WRT the number of authentic coins, since it's impossible to tell from one scale reading whether you had false coins whose errors cancelled or whether you have authentic coins.
    Here is my take on this.

    Actually, the puzzle says that each fake coin is +/- .01 of a real coin. However, it also says all the coins in an individual chest are identical. So, if one coin in a chest is -.01 of a real coin, then they must all be. Therefore, solving the puzzle should involve taking a set of coins from each chest such that if a chest holds fake coins will be identifiable based on the value away from the expected total it is.

    Chest 1: 1 coin
    Chest 2: 3 coins
    Chest 3: 5 coins
    Chest 4: 7 coins
    Chest 5: 9 coins
    Expected if all are real = 25
    24.9 or 25.1 would mean all are real but chest 1. If the difference is exatly .3 then only chest two. If the difference is .4 or .2, then chest 1 and 2 are fake. And so on. I realize I am off by a factor of 10. I also believe the values may need to be prime numbers. So, instead of 9, then 11. I have not tested this all the way through.
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  5. #4
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    Re: The Leprechaun's Challenge

    I could sue him for plagiarizing Tolkien and then I wouldn't have to weigh the coins?
    "Suffering lies not with inequality, but with dependence." -Voltaire
    "Fallacies do not cease to be fallacies because they become fashions. -G.K. Chesterton
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  6. #5
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    Re: The Leprechaun's Challenge

    Ibelsd, You are on the right track.

    Squatch, I'm unfamiliar with anything remotely similar to this in any of Tolkien, but I've only read the Hobbit and part of the Silmarillion. (I've had the full set of Lord of the Rings since junior high and have never yet read it. Shameful, I know.) Could you provide a more specific reference to to the material you think this plagiarizes?

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  8. #6
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    Re: The Leprechaun's Challenge

    Quote Originally Posted by Galendir View Post
    Squatch, I'm unfamiliar with anything remotely similar to this in any of Tolkien, but I've only read the Hobbit and part of the Silmarillion. (I've had the full set of Lord of the Rings since junior high and have never yet read it. Shameful, I know.) Could you provide a more specific reference to to the material you think this plagiarizes?
    I was being somewhat facetious, sometimes the jokes fall a bit flat on the internet sorry. I meant to play off the phrase "But not all that glitters is gold..." which is similar to Tolkein's poem:

    All that is gold does not glitter,
    Not all those who wander are lost;
    The old that is strong does not wither,
    Deep roots are not reached by the frost.
    From the ashes a fire shall be woken,
    A light from the shadows shall spring;
    Renewed shall be the blade that was broken,
    The crownless again shall be king.
    https://en.wikipedia.org/wiki/All_th...es_not_glitter

    [Though to be appropriately critical of myself, I didn't realize the phrase originated with (or before) Aesop.]
    "Suffering lies not with inequality, but with dependence." -Voltaire
    "Fallacies do not cease to be fallacies because they become fashions. -G.K. Chesterton
    Also, if you think I've overlooked your post please shoot me a PM, I'm not intentionally ignoring you.


 

 

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