Puzzle: find the odd coin (very difficult)?

Question

you have 12 _very rare_ coins
one of the coins is a forgery..... it is an almost perfect replica, except that it is made from a different alloy from the originals.
you do not know if the fake coin is _heavier_ or _lighter_.

you have use of a balance scale (a scale which weighs one side against the other) but can only use it for 3 seperate weighings

how do you identify the odd coin?

10 pts to the first correct answer

First 3 answers are no go.
Clue:
if you weigh 6 coins on side A against 6 coins on side B - and side B goes down, It doesnt show whether the fake is a heavier alloy (and is therefore on side B) or a lighter alloy (and is therefore on side A)

Blinky, I think your method was disproved by Galileo, about five hundred years ago.

Answer 1

There is no point weighting half of the coins to each side cuz u kno one side is gona be heavier than the other and u still wont kno which one contains the fake.
1. Put 4 coins on each side:
A. If they balance, take 3 out of the 4 which were left out and weight them against 3 real ones, if it balances the one left out is the fake. If not, u will know whether the fake is heavier or lighter, then weight the 2 out of the 3 that contains the fake against each other, if it balances the one left out will be fake. If not u will know whether the fake one is the heavier or lighter.
B. If they dont balance, take two from the heavy side and one from the light side and weight it against one heavy one light and one real.
B1. if they balance, take the two from the lighter pile out of the three that were left out, if they balance the one left out is the fake if they dont the lighter one is the fake.
B2. if the side with two heavys and one light is heavier, either one of the two heavy ones is heavy or the light on the other side is light, so weight the two heavy ones against each other if they balance the light one is fake if not the heavier one is fake.
B3. if the side with one real, one haevy and one light is heavier, either the heavy on the heavier side is fake or the light on the lighter side is fake, weight the light one with a real coin, if it balances the fake is the one left out if not the lighter one will be fake.

Shiiit it took me quite a long time to get thru this but i think its rite

Answer 2

Split the coins into 3 piles of four.
weigh 2 piles, if there equal, then the other pile contains the fake
remove one pile and substitute the unweighed pile, this will determine if the fake is heavier or lighter.

if not equal substitute the unweighed pile, if the scales balance then the fake is in the removed pile and you also know if it is heavier or lighter, if they don't balance a second time the fake is in the pile that was left on the scale and you also know if it is heavier or lighter.

that's 2 weighs to get to 4 coins of which we know the fake is in and we know if it's heavier or lighter

now put 2 on either side from our fake pile of 4, then remove one from either side, if the scale balances then the fake was on the lighter/heavier side- all ready known- and was just removed, if not it is the one remaining on the scale

technically this may be 4 weighs

Answer 3

Some of the answers given seem to make sense except that none of the answer the question "Is the fake coin lighter or heavier?" Given the answer to that question there are a couple of ways to determine which coin is fake in just 3 measurements. Since we don't know, the whole thing becomes way more complicated.

I attached a link where a bunch of mathmaticians attempted to solve this riddle. Enjoy.

Answer 4

Split the coins into 3 sets of 4 choose 2 of the sets if they weigh the same then the odd coin is in the other set. chuck out one set and then take away two coins from the other set then get two coins from the pile with the fake coin in it and put it in the empty side. if the scale does balance then take on out of one side then get one of the reminig two if it balances then the remaining one is the fake if it doesn't the one out of the remaining pile you put on last is the fake.

Answer 5

split the coins into 3 piles of 4. weigh a pair of piles against each other and if they balance, they other pile has the odd coin. split the odd pile in half and put one half onto the scale, take two of the coins from the real pile and weigh them against it. if it balances then the odd coin is in the 2 you set aside. if it doesnt it is on the scale. if its on the scale you take away one coin from each pile on the scale and if it balances then the coin you took away was the fake, if it doesnt the fakes still onthe scale. and you just identified it.

if the piles of two had of balanced, then the coin was on the pile off the scale, so you now weigh one coin from the odd pair on the side and one coin that you know is real. if it balances, the fakes on the side, if it doesnt the fakes on the scale.

whew, i hope it actually works...

Answer 6

in the fiest weighing u put on 6 coins and 6 coins whever 1 is lighter u keep them coins divide them into 3 coins and 3 coins then which one is lighter 3 is lighter u keep them then u feel them and u can tell from the smaller amount of coins which 1 is lighter that is the lighter coin

Answer 7

1. put half on one side, half on the other
2. with the heavier half, put half on one side one on the other.
3. with the 3 heavier coins remaining put on one side, one on the other. If these two even out, then the third remaining coin (not weighed) is the forgery.



Just realised I was wrong..... It appears Blue Seahorse has it. Good stuff.

Answer 8

Weigh out 6 in each side. lighter side will go up.
Weigh those 6 as 3 each side... lighter side will go up

Weigh one each side.. if even the coin left off is fake. if side goes up, light one is fake.

Answer 9

Heat them, different alloys will have different melting points, except you might not have a coin left at the end.

Answer 10

Take them to a bank to get them exchanged, and which ever one they give you back and possibly arrest you for is the fake...simple yet effective....i don't get the crack with the scales whats it going to do if you weigh 4 times....self destruct in 5 seconds!