# Teaser #6

#### ban-all-sheds

Like most teasers, the answer is probably out there on the internet, so if you can't be bothered to work it out, please leave it for others.

You have 12 coins, one of which is fake, and is either slightly heavier or slightly lighter than the real ones, but otherwise identical.

You have a pair of balance scales.

In 3 weighings you must identify the fake coin, and tell whether it is heavier or lighter.

How?

ive not got the answer but im finkin, split into 3 groups of 4, weigh 2 sets if there the same its in the last 4 if its not the same add the other 4 to any of the other 4 and if it goes up or down its that one group of 4 if you know what i mean. so thats either one weigh in or 2. then your left with four, 1 against another if they weigh the same its one of the other two if they dont your ****ed

2 weighings have got to be the same.the third will tell you if it's heavier or lighter.....

just give us a minute to figure the rest out?

for the first weighing, can the coins be added to the scales two at a time, one on each tray?

'cause you could narrow it down to two this way.

noseall said:
for the first weighing, can the coins be added to the scales two at a time, one on each tray?
No - each time you add coins that's another weighing.

split into 2 sets of 5 if they weigh the same its one of the other two, done in one weigh in how do you find out which ones the fake the heavy one or light one, im working on it

your left with 2 coins, take a coin out of the five and add one of the coins so its 5 against 5 if its equal the coin youve got left is fake ive done it in 2 weigh ins

I can do it IF you know whether the fake is heavier or lighter in advance, but I'm really struggling with it as it is.....

For example, if you knew the fake was heavier:

Divide into 3 x 4 called G1, G2 and G3

Weigh G1 against G2. Either the heavier of those two contains the fake or, if the same then G3 contains the fake.

Take 2 coins from a known 'good' pile and measure against two from the 'fake' pile. If they match, the remaining two have the fake, or you will identify the fake as being the heavier one on the balances.

Do the same again with one good against one of the 'fake' pair and voila.

But, say you get the fake one of the sets on the scales in the first step, and you don't know if its heavier or lighter, then you're stuck without doing extra weighings.

jbonding said:
What if you're not? What if the 5 v 5 didn't balance?

take a coin out of the five and add one of the coins so its 5 against 5 if its equal the coin youve got left is fake
What if it's not?

ive done it in 2 weigh ins
No - even if you had been lucky enough to get this far you still haven't found out if it's heavy or light.

ban-all-sheds said:
jbonding said:
What if you're not? What if the 5 v 5 didn't balance?

take a coin out of the five and add one of the coins so its 5 against 5 if its equal the coin youve got left is fake
What if it's not?

ive done it in 2 weigh ins
No - even if you had been lucky enough to get this far you still haven't found out if it's heavy or light.

in my test i was lucky enough to get this far was left with 2 coins having only done one weigh in which determined the 10 coins i weighed against each other were equal meaning the fake wasnt in there so that means its one of the other 2 ive got left do you agree. ive taken one of the 2 coins and replaced it with another coin in the ten and weighed them against each other, 5 against 5 and they were equal so that means the fake is the last coin regardless of its weight if we are to beleive one is a fake and difers in weight from the rest so that means its possible to do it in 2 weigh ins

just read it again and noticed this,
"In 3 weighings you must identify the fake coin, and tell whether it is heavier or lighter. "

so i have to use my extra weigh in so i will try the last coin in one of the 5 and weigh against the other 5 and if it goes up or down that is the answer, i thank you

ban-all-sheds said:
jbonding said:
What if you're not? What if the 5 v 5 didn't balance?

take a coin out of the five and add one of the coins so its 5 against 5 if its equal the coin youve got left is fake
What if it's not?
ive done it in 2 weigh ins
No - even if you had been lucky enough to get this far you still haven't found out if it's heavy or light.

well if its not and it goes down or up it means weve found the fake and can determine its weight in 2 weigh ins but what are the chances of doing that on your first go

It's no good - I'm too tired to work out if you're having a laugh or have utterly failed to understand the Q......

ban-all-sheds said:
It's no good - I'm too tired to work out if you're having a laugh or have utterly failed to understand the Q......

ive finally worn you out seriously i think ive got it

OK - what's the answer then - one that will always work, and does not depend on luck....

Split them into 4 groups of 3 (G1, G2, G3 and G4)

Weighing 1)

Measure G1 against G2.

If G1 = G2 then.....

Weighing 2)

Measure G2 against G3

If they are the same, then G4 contains the fake, if not then G3 does

(or if at weighing 1 then G1 not = G2 then make weighing 2 G2 against G3 and identify the fake pile from G1 or G2 accordingly).

At this stage, you will also have worked out if the fake is heavier or lighter by what has happened in the weighings so far.

Weighing 3)

take two coins from the fake pile of 3 and meaure them against each other. If the same then the third coin is the fake. If there is an imbalance then you worked out whether the fake was lighter or heavier after weighing 2 so will know what it is.

Have I got it ??

EDIT: Actually this falls down if the fake coin is in G4, as you then don't know if the fake is heavier or lighter. More thinking required.....

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