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The Bad Penny puzzle

 
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IQofaGerbil

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Joined: 05 May 2006
Posts: 183
Location: Scotland

PostPosted: Mon Jun 26, 2006 8:03 pm    Post subject: The Bad Penny puzzle
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You have 12 coins.
One of the coins is ‘bad’
The bad coin is either heavier or lighter than all of the others.

You have to
a) identify the bad coin
and
b) determine whether it is lighter or heavier than the others.

In order to help, you have one set of balance scales.

You can use the scales up to (but not more than) three times.

Go figure!
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Lamichka

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Joined: 16 May 2006
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Location: CZ

PostPosted: Tue Jun 27, 2006 8:16 am    Post subject: It's easy
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You'll chose random 2 sets of 4 coins.

If the scale is equal the bad coin is in the last set of coins.
Else you'll have one side lighter and you'll choose the lighter set of coins.

Now you have four.

the rest is easy.
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IQofaGerbil

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PostPosted: Tue Jun 27, 2006 3:30 pm    Post subject: Re: The Bad Penny puzzle
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Why would you choose the lighter set of coins?
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IQofaGerbil

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PostPosted: Tue Jun 27, 2006 9:15 pm    Post subject: Re: The Bad Penny puzzle
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Lamichka -

after you have chosen the lighter you say that you would easily find the bad coin, but what if the bad coin is heavy and not light, then you will have chosen the wrong set! Then what?

So maybe the rest is not so easy!!!


Go figure
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cpuhawg

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Joined: 14 Jun 2006
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Location: Jacksonville, FL

PostPosted: Wed Jun 28, 2006 7:44 pm    Post subject:
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12 coins
Each coin either G (good), H (heavy bad), or L (light bad)

The solution can be found during the last weighing once you have eliminated 9 of the coins (because they are good) and being left with 3 coins that are either G (good) or H (heavy) or??. G (good) or L (light)

1st Weigh 4 and 4 (equal)
8 that were weighed are G because the scale was equal.
If equal, then last remaining 4 are (G, H, or L)
2nd Weigh 3 G against 3 that are (G, H, or L).
-If equal, then 11 are now G and 1 is (G, H, or L) and your 3rd weigh will be a G against the remaining (G, H, or L) and you should find the answer
-If not equal, then 9 are now G and the last 3 are either (G or H) ....or (G or L) (depending on which way the scale tipped).
3rd Weigh would be a G and a (G or L) against a G and a (G or L). If one side goes up, you've identified the light coin. If they are equal, the coin not being weighed is Light.
3rd Weigh could also be a G and a (G or H) against a G and a (G or H). If one side goes down, you've identified the heavy coin. If the other side goes down, you?ve located the heavy coin. If they are equal, the coin not being weighed is Heavy.

1st Weigh 4 and 4 (not equal)
4 not weighed are G
4 are (G or L)
4 are (G or H)
2nd Weigh (left side) 3 G and 1 (G or L) against (right side) 3 (G or L) and 1 (G or H)

- If equal, then you now have 9 G and 3 (G or H).
3rd Weigh would be a G and a (G or H) against a G and a (G or H). If one side goes down, you've identified the heavy coin. If the other side goes down, you?ve located the heavy coin. If they are equal, the coin not being weighed is Heavy.

- If not equal?.
If the left side tips up up from the 2nd weigh, you now have 10 (G), 1 (G or L), and 1 (G or H) ? (Light coin makes the left tip up or Heavy coin makes the right tip down).
3rd weigh would be one G against 1 (G or L) and if equal, you located the heavy coin. If not equal, you?ve located the light coin.
If the right side tips up from the 2nd weigh, you now have 9 (G) and 3 (G or L)
3rd Weigh would be a G and a (G or L) against a G and a (G or L). If one side goes up, you've identified the light coin. If they are equal, the coin not being weighed is Light.
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IQofaGerbil

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PostPosted: Wed Jun 28, 2006 8:51 pm    Post subject: Re: The Bad Penny puzzle
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Looks good to me
How long did it take you to solve it? I have some freinds who gave up after many hours of trying!!!

I have a slightly different solution because I like to always keep 4 coins on each side when weighing ;


Coins are A B C D E F G H I J K L


Weigh A B C D against E F G H

If both are equal,
Then one of I J K L is the odd coin so,
Weigh E F G I against J K A B
If left side is lighter than right side then either I is light or (J or K) is heavy
So then weigh E F G J against A B C K
If left is lighter than right then K is heavy
If left heavier than right then J is heavy
If left = right then I is light
Else if left side = right side then L is the odd coin
So weigh A B C L against E F G H
If left is light then L is light
If left is heavy then L is heavy

Else
If A B C D is lighter than E F G H
Then one of the left coins is light or one of the right coins is heavy so,
Weigh A E F G against H I J K

If both are equal then one of B C D are light so
Weigh E F G B against I J K C
If left is light then B is light
If right is light then C is light
If both equal then D is light

Else
If left is light then either A is light or H is heavy so
Weigh A B C D against I J K L
If left is light then A is light
If both are equal then H is heavy
Else
If left is heavy then one of E F G is heavy so
Weigh A B C E against I J K F
If left is heavy then E is heavy
If right is heavy then F is heavy
If both equal then G is heavy
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cpuhawg

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Joined: 14 Jun 2006
Posts: 331
Location: Jacksonville, FL

PostPosted: Wed Jun 28, 2006 10:59 pm    Post subject: Re: The Bad Penny puzzle
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Your solution looks good as well. It took me about 5 hours of working on and off.
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