Brain Teaser

[MetalGrasshopper]

I have 8 identical bags of coins. I know that 7 contain the same number of coins and 1 bag is missing a coin. The only tool available to me is a balance (like the one on the cover of ...And Justice For All). How would I, without opening any of the bags, determine which bag is missing the coin if I'm allowed to use the balance only twice?

[RacerX]

Re: Brain Teaser

Answer: On the scale, place 1 coin from the first bag, 2 coins from the second bag, and so on ending with 10 coins from the tenth bag. You end up with 55 coins on the scale. It they were all genuine, they would weigh 550 grams. If they weigh only 547 grams, then 3 of the coins must be counterfeit, so the third bad contains the counterfeit coins. If they weigh 546 grams, then 4 of the coins are counterfeit, so the fourth bag contains the counterfeit coins...

[img]/images/graemlins/tongue.gif[/img]

[diablomozart]

Re: Brain Teaser

First let's number the coins from 1 to 8 to help us describe a pair of weighings that work. In the first weighing, balance coins (1, 2, 3) on the left against coins (4, 5, 6) on the right. Whatever the outcome, in the second weighing balance coins (1, 4, 7) against (2, 5, 8). That's it.




If the left side of the balance is heavier for both weighings (HH), then coin 1 is the heavier coin because it's the only one on the left side for both weighings. If the left side is heavier for the first weighing, but lighter for the second (HL), then coin 2 is the heavier coin because it's the only one that's on the left side for the first weighing and the right side for the second. If the left side is heavier for the first weighing and equal in weight for the second, then coin 3 is the heavier coin for similar reasons.

...d.m.

[toejam]

Re: Brain Teaser

How big are the coins and how much are they worth? [img]/images/graemlins/laugh.gif[/img]

[AK47]

Re: Brain Teaser

Its bags of coins.
You weigh six bags and set two bags to the side.
If the three on each side of the scale weigh equal you eliminate six bags. weigh the last two and you find the lighter one is missing a coin.

Now if you are weighing six bags three on each side and one side is lighter you take those three bags set them for the second weigh in because one is missing the coin.

Take two bags and weigh them. If they are equal your last bag is the one missing a coin or the lighter bag on the scale is missing a coin.

From years of weighing crap this is easy for me.

[AK47]

Re: Brain Teaser

Diable Mozart did get it right before me he just used the word coins instead of bags of coins. I skipped over his post when I read just the word coins so I assumed he got it wrong.

[quadperson]

Re: Brain Teaser

huh???

[zeegler]

Re: Brain Teaser

[ QUOTE ]
Its bags of coins.
You weigh six bags and set two bags to the side.
If the three on each side of the scale weigh equal you eliminate six bags. weigh the last two and you find the lighter one is missing a coin.

Now if you are weighing six bags three on each side and one side is lighter you take those three bags set them for the second weigh in because one is missing the coin.

Take two bags and weigh them. If they are equal your last bag is the one missing a coin or the lighter bag on the scale is missing a coin.

From years of weighing crap this is easy for me.

[/ QUOTE ]

Just what exactly have you been weighing??? [img]/images/graemlins/brow.gif[/img] [img]/images/graemlins/brow.gif[/img] [img]/images/graemlins/grin.gif[/img]

[Newc]

Re: Brain Teaser

[ QUOTE ]
I have 8 identical bags of coins. I know that 7 contain the same number of coins and 1 bag is missing a coin.

[/ QUOTE ]

Then the bags are not identical, therefore the question is invalid [img]/images/graemlins/laugh.gif[/img]

Begin: Put 4 bags on each side of the scale - the lighter side will be the one with the missing coin.
1st Use of the scale: Remove 2 bags from each side. If the scales are unbalanced, the lighter bag is still on the scale. If the scale balances, one of the two bags you removed from the lighter side is missing a coin.
2nd Use of the scale: If the scale is balanced with 2 bags on each side, swap one bag on the scale with one of the ones you took from the lighter side previously. If the scale is then unbalanced, the bag you put on is missing one coin. If the scale is then still balanced, the other bag you took off in the first use is missing the coin.

It's a bit of a trick question because it doesn't specify what constitutes taking a turn on the scale. Most automatically assume that if you put any bags on each side of the scale, you've used your first turn and can only take one more action (swapping bags or whatnot). In order to be a solvable puzzle, one concession must be allowed - putting all 8 bags on the scale first (IF they're not already there). Anything after that counts as the first turn.

[YetAnotherOne]

Re: Brain Teaser

[ QUOTE ]
Then the bags are not identical, therefore the question is invalid [img]/images/graemlins/laugh.gif[/img]

[/ QUOTE ]

Y'know, there's nothing stopping the bags from being identical even if they don't happen to contain the same amount of coins. [img]/images/graemlins/grin.gif[/img]

[followthereaper]

Re: Brain Teaser

[ QUOTE ]
[ QUOTE ]
I have 8 identical bags of coins. I know that 7 contain the same number of coins and 1 bag is missing a coin.

[/ QUOTE ]

Then the bags are not identical, therefore the question is invalid [img]/images/graemlins/laugh.gif[/img]

Begin: Put 4 bags on each side of the scale - the lighter side will be the one with the missing coin.
1st Use of the scale: Remove 2 bags from each side. If the scales are unbalanced, the lighter bag is still on the scale. If the scale balances, one of the two bags you removed from the lighter side is missing a coin.
2nd Use of the scale: If the scale is balanced with 2 bags on each side, swap one bag on the scale with one of the ones you took from the lighter side previously. If the scale is then unbalanced, the bag you put on is missing one coin. If the scale is then still balanced, the other bag you took off in the first use is missing the coin.

It's a bit of a trick question because it doesn't specify what constitutes taking a turn on the scale. Most automatically assume that if you put any bags on each side of the scale, you've used your first turn and can only take one more action (swapping bags or whatnot). In order to be a solvable puzzle, one concession must be allowed - putting all 8 bags on the scale first (IF they're not already there). Anything after that counts as the first turn.

[/ QUOTE ]

That's what I came up with. I don't get why the moron in the problem doesn't have an electric balance?

[VitaminG]

Re: Brain Teaser

[ QUOTE ]
How big are the coins and how much are they worth? [img]/images/graemlins/laugh.gif[/img]

[/ QUOTE ]
more importantly - how fast is the treadmill travelling?

[diablomozart]

Re: Brain Teaser

i was stoned...sorry...lol...d.m.

[Markus]

Re: Brain Teaser

[ QUOTE ]
Its bags of coins.
You weigh six bags and set two bags to the side.
If the three on each side of the scale weigh equal you eliminate six bags. weigh the last two and you find the lighter one is missing a coin.

Now if you are weighing six bags three on each side and one side is lighter you take those three bags set them for the second weigh in because one is missing the coin.

Take two bags and weigh them. If they are equal your last bag is the one missing a coin or the lighter bag on the scale is missing a coin.

From years of weighing crap this is easy for me.

[/ QUOTE ]

Good call!!! I have a minor in Mathematics, and love logic problems like this. Nice solve.

-Mark

[GodOfRhythm]

Re: Brain Teaser

Wait wait, are the coins being considered relative to the ground or to the airspeed of the balance?