weights and measures

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weights and measures

Postby Hud » Sun Jul 02, 2006 5:21 pm

Here's one I just thought up. It might require some local knowledge, but possibly not.

I have 10, 1982 U.S. Pennies
One is more valuable that any other one
Using a simple balance mechanism, What is the minimum number of balance tries required to find the most valuable penny?
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Postby underquark » Sun Jul 02, 2006 5:39 pm

Wikipedia wrote:The cent's composition was changed in 1982 because the value of the copper in the coin started to rise above one cent. Some 1982 cents use the 97.6% zinc composition, while others used the 95% copper composition.
So, one out of the ten is either heavier or lighter than the others?
Last edited by underquark on Sun Jul 02, 2006 3:18 pm, edited 1 time in total.
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Re: weights and measures

Postby lunababy_moonchild » Sun Jul 02, 2006 6:15 pm

Hud wrote:Here's one I just thought up. It might require some local knowledge, but possibly not.

I have 10, 1982 U.S. Pennies
One is more valuable that any other one
Using a simple balance mechanism, What is the minimum number of balance tries required to find the most valuable penny?

I reckon it's 9.

Luna
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Postby coloin » Sun Jul 02, 2006 6:52 pm

I tink it might be a maximum of 3.
Four fifths of the time it can be done in 2.

First weighing - slplit into 3 piles

3^3...or its in the 4 pile of coins


if in one of the 3 piles
1^1 or 1 identified in 2 weighings

if in one of the 4 piles

1^1 identified in 2 weighings

1^1 needs the 3 weighing here

C
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Postby ronk » Sun Jul 02, 2006 7:09 pm

coloin wrote:I tink it might be a maximum of 3.
Four fifths of the time it can be done in 2.

Even one fifth is better than "five sixths.":)
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Postby underquark » Sun Jul 02, 2006 7:32 pm

3 weighings would identify the odd-one out. Assuming the valuable one is very slightly heavier (3.1g v 2.5g):

1] Weigh 2 piles of 5 and discard the lighter pile.
2] Weigh 2 piles of 2 and set one penny to one side; either keep the heavier pile or (if equal weight) keep the penny on the side which must be the vluable copper-rich one.
3] If you had a heavier pile at stage two then balance the two off and keep the heavier one. You have now found a 1¢ coin containing just over 2¢ worth of copper.

BUT! What if you have one of the rare - and lighter - 1974 Aluminum ones? Aaprt from it being a Federal Offence to be in possession of one, how can you tell if your pile of 10 has a heavy one or a light one in it?
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Postby Hud » Sun Jul 02, 2006 8:06 pm

underquark, I think you know more about pennies than 95% of Americans do. I started saving the copper pennies when they switched to the mostly zinc variety. I have around 3 or 4 1 gallon paint cans full not. The 1982 ones make me use a popsicle stick and a pencil to see if they are the good ones.
Now I have to try to figure out the one with the Aluminum penny in it.
By the way, I once worked with a guy from England who always said "Aluminium". I thought he was kidding til he wrote it that way on a drawing.
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Postby coloin » Sun Jul 02, 2006 8:53 pm

underquark wrote:BUT! What if you have one of the rare - and lighter - 1974 Aluminum ones? Aaprt from it being a Federal Offence to be in possession of one, how can you tell if your pile of 10 has a heavy one or a light one in it?


Ah.... a bit trickier.

[Do they have Pennies instead of Cents in Arizona ?]

But I think you should still be able to do it in 3 weighings.

1.Weigh 3^3

2a If equal
the different coin is in the 4 pile - weigh 3 from the 4 pile against 3 normal coins
-----If equal then the other coin[of the 4] is different
-----If unequal
-----------------If heavier the heavier coin is in the heavy 3 pile -
-----------------If lighter then the lighter coin is in the lighter 3 pile


2b If unequal
compare the heavy pile of 3 with 3 normal ones.
--------------if this equal then the light coin is in the other lighter 3 pile
--------------if this is unequal then the heavy coin is in the heavier 3 pile


3 one more weighing needed in each case


The above logic asumes there is one different coin and nine similar ones. [Uniqueness ?]

What if Hud got it wrong and there was 2 heavy coins and 8 normal ones, how many weighings quarentee identification. ?
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Postby Hud » Sun Jul 02, 2006 9:09 pm

Dammit, coloin, I just figured out the last one and you have to add another.
We do use "penny" more often than "one cent".
While "whilst" we're on this subject, I recently found a coin that looked almost exactly like one of our "dimes" (ten cent piece) next to one of those coin exchanging machines at a super market here. I suppose the machine rejected it since it was a bit thicker than a dime. I've been using it as a ball marker at golf, but it hasn't helped my game much.
the coins has these markings:

1. Head of Queen Elizabeth on front
2. Crown and some leaves (possibly oak leaves) on back
3. Elizabeth II D G Reg F D 2000 on front
4. Five Pence 5 on rear.

I'm assuming I'm not rich by finding this, but is it worth approximately 10 cents US?

By the way, the coin exchanging machines charge almost 10% for exchanging the coins.
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Postby underquark » Sun Jul 02, 2006 11:25 pm

Image
You picked a germane example. The UK used to have Pounds, Shillings and Pennies with 12 pennies to the shilling, 20 shillings to the pound (that's 240 pennies to the pound). Along came the metric system and then decimal currency on 15 February 1971 (I still vaguely remember it) and 240 pennies to the pound became 100. A shilling became 5 New Pence (later just 5 Pence).

Shillings used to be made of Silver (you can keep your cheap copper rubbish) from about 1630 to 1947 and measured 1" (one inch) in diameter. After 1947 they switched to copper/nickel. When decimilisation came along the old shillings were replaced by "5 New Pence" pieces of exactly the same size, later (1981) simplified to just "5 Pence" and then - in 1990, to save money - they were simply halved in size.

The 10 Pence piece was also shrunk - to the size of the former shilling. Thus, although the UK has decimal currency and embraced the metre, kilogram and litre, our 10 Pence pieces still measure exactly one inch across.
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Postby udosuk » Mon Jul 03, 2006 12:11 am

This describes the situation with aluminium or aluminum... It seems the North Americans are (again) doing something different to the rest of the world... I can assure you in Australia we use Aluminium, which is the way we're taught in schools and universities...

If you have exactly 1 different coin (heavier or lighter, we don't know) out of 12 coins, only 3 balancings are enough to pick it out.
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Postby Hud » Mon Jul 03, 2006 12:47 am

I wonder why we got started dropping an "i" from aluminium? We accept ium for other elements like:
Radium
Uranium
Einsteinium
Tellerium
Platinium, oops, that one slipped by.

With two of ten coins of the heavier variety, I need 5 weighings to sort out the two copper ones.
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Postby udosuk » Mon Jul 03, 2006 1:25 am

Hud wrote:With two of ten coins of the heavier variety, I need 5 weighings to sort out the two copper ones.

I thought that too, but then I realized the 2 heavier coins could be of different weights themselves...
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Postby r.e.s. » Mon Jul 03, 2006 2:24 am

Hud wrote:I wonder why we got started dropping an "i" from aluminium? [...]

There's an interesting article at
http://www.worldwidewords.org/articles/aluminium.htm

Apparently it was first named alumium, then aluminum, then aluminium, then (in USA) back to aluminum!
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Postby udosuk » Mon Jul 03, 2006 3:30 am

And the British call it sulphur, Americans call it sulfur, while in Australia we seem to use both (but I think in my hometown we use sulphur more). The international authorities use sulfur... So it seems USA wins this time...

Interestingly a few cities in USA are named Sulphur...

I suppose the use of the ph could have some association to the acidity meaning (probably not)...:?:
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