Twelve Coins?

Question

You have twelve coins, eleven identical and one different. You do not know whether the "odd" coin is lighter or heavier than the others. Someone gives you a balance and three chances to use it. The question is: How can you make just three weighings on the balance and find out not only which coin is the "odd" coin, but also whether it's heavier or lighter?

Answer 1

5. This is a real toughie. Along the way, we'll denote coins
we know nothing about with '?'; coins that can't be the odd
coin with '0'; coins that must be heavier if they're odd with 'H';
and coins that must be lighter if they're odd with 'L'.
STEP 1. Weigh four coins against four coins. Either (a) they
balance or (b) they don't. So (a) looks like 00000000???? and (b)
looks like HHHHLLLL0000.
STEP 2(a). Weigh two '?' coins against one '?' and one '0'.
There are three possible results: (i) they balance, (ii) the '??'
side is heavier, (iii) the '?0' side is heavier.
STEP 3(a)(i). Since the scales balanced again, we now have
00000000000?. The last coin must be the odd coin. Weigh it against
an '0' coin to see whether it's too heavy or too light.
STEP 3(a)(ii). The 4 coins not weighed in step 1 now are HHL0.
Weigh H against H. If the scales balance, L is the odd coin and is lighter
than the other coins. Otherwise, the tip of the scale tells you which
is H is in fact heavier and which is actually an 0 coin.
STEP 3(a)(iii). Proceed as in 3(a)(ii), but with L's and H's switched.
STEP 2(b). We so far have HHHHLLLL0000. Weigh HHL against HL0.
There are three possible results: (i) they balance, (ii) the 'HHL'
side is heavier, (iii) the 'HLO' side is heavier.
STEP 3(b)(i). The five "candidate" coins on the scale in the last
step must be ok, leaving HLL000000000. Proceed as in step 3(a)(iii).
STEP 3(b)(ii). The three "candidate" coins not weighed in the
last step must be ok. Also, since HHL was heavier than HL0, either
an H from the left side is truly heavier or the L on the right
side is truly lighter. This gives HHL000000000, so proceed as
in step 3(a)(ii).
STEP 3(b)(iii). Again, the three "candidate" coins not weighed
in step 2(b) are ok. Since HL0 was heavier than HHL, either
the H on the left is truly heavier or the L on the right is
truly lighter. Weigh the H coin against any 0 coin. If they
balance, the L is truly lighter; if not, the H is truly heavier
(and the scale will tip toward H).

Answer 2

okay, here goes... (partial solution??)

split coins into three piles of four,
weigh two sets of four coins:

if the scale DOES balance then the fake is in the four remaining,
take all four coins away from one side and discard them,
take away two coins from the other side...
put two coins from the pile of four (one of which is fake,)
on the empty side,

if the scale doesn't balance then note if it goes up or down, if up then coin is lighter if down coin is heavier. Split the two coins from the side that contains the fake, one on each side, if you noted that the fake was heavier choose the coin that goes down if the fake was lighter choose the coin that goes up.

However, if the scale balances after the second weighing then you know one of the two remaining coins is fake. Place one the scale against one of known good coins. if up lighter if not heavier. If scale balances AGAIN then the remaining coin is fake however you do not know if it is heavier or lighter

Answer 3

one of them is different, so u weigh it then weigh any of the other 11 identical coins!!

Answer 4

why shld I?