OK, wanna try a cool problem to solve?

Question

here you go:

You have 12 coins. One of these coins is a fake. It differs from the rest only by it's weight. You don't know whether it is lighter or heavier the the rest of the coins.
You also have a scale, but not the electronic one, the two-cups one, with which you can only tell which cup has more or less weight.
And you only have 3 times to weight the coins to find out which one is a fake.
Remember once again : YOU DON'T KNOW IF THE FAKE COIN IS LIGHTER OR HEAVIER THE THE REST. ONLY 3 WEIGHS.
Solve that! :))))

P.S. Took me 2 weeks to solve. I thought about every day for a couple of hours per day.

I REPEAT:!!!!!!
YOU DON'T KNOW IF THE FAKE COIN IS LIGHTER OR HEAVIER THE THE REST

Answer 1

My best attempt:

Weigh four on one side, four on the other side. Reserve the last four.
If left goes up, label each left coin A and each right coin B. Label reserved coins N
If it balances, relabel each reserved coin to C and all other coins N

Step 2:
If coins labeled A weigh A A N ^ N N N.
Reserve the other two A coins and relabel them AR.
2a. if left side goes up, relabel each coin with A to AL.
2b. if left side goes down, relabel each scale coin A to AH.
2c. if it balances, relabel the A coins on the balance to N.

Follow same procedure if you have B or C coins.

You should now have two coins marked ?R, ?L, ?H
where ? = A or B or C

Step 3:
If coins are labeled ?R, relabel with ?R1 and ?R2
weigh ?R1 ^ N, reserving ?R2
if it balances, ?R2 is a fake
if it doesn't balance, ?R1 is a fake

If coins are labeled ?L, relabel with ?L1 and ?L2
weigh ?L1 ^ N, reserving ?L2
if it balances, ?L2 is a light fake
if it doesn't balance, ?L1 is a light fake

If coins are labeled ?H, relabel with ?H1 and ?H2
weigh ?H1 ^ N, reserving ?H2
if it balances, ?H2 is a heavy fake
if it doesn't balance, ?H1 is a heavy fake

Hope I'm right!

Answer 2

Yeah, the first two people who answered the question definitely missed the part about not knowing whether the coin is lighter or heavier even though he wrote it twice, once in all caps. Sounds like a pretty difficult problem. The pompous girl who said she figured it out in a minute or so is an idiot.

Answer 3

Weigh 6 coins on each side, take the coins from the heavier side and put 3 in each cup. Now with three left pick any two and put one in each cup, if one is heavier that's the coin, if they are equal then the heavier coin is the one thats left. That took me about a minute to figure out, in case you were wondering, good problem.

Answer 4

for the ones above who answered this, what if the cup you chose to weigh was the wrong cup? say, the lighter cup you chose to weigh was only lighter because the coin was heavier, thus making that cup heavier, and the cup you chose to weigh lighter? or vise-versa? your way is FLAWED. and as for the first person, in my opinion, you sound like you think very highly of yourself. stop it. you arent the best person in the world. i am.

Answer 5

first divide coins in half and weigh
one will be lighter
divide the lighter in half again and weigh
take that lighter half (should be 3)
weigh two coins if they weigh the same the odd one out is your fake otherwise one will show lighter
will apply if its heavier too

Answer 6

Go to a old time candy store and use the coins there trust me they don't care which is fake