12 coins by engiin!!

Hello all!

I don't think we should weight them all together. Wouldn't it be easier to take three coins and see if there is any possibility for the "different" coin to be one of those? If it is different, it should weight more or less than the others, this way would be much easier..

Then, well done!

Nope..In probability you have to consider all the options and then multiply them all.

Wouldn't it be something like this if there is no return of coins?

1/12 x 11/11 x 10/10 + 11/12 x 1/11 x 10/10 + 11/12 x 10/11 x 1/10

Damn this thread. I noticed  this problem and wanted to solve it. I lost a lot of time, now I demand a refund!

It is difficult to explain though. I'll try...

You start by weighing 4 coins on each plate (1st step).
If they balance the different coin is among the other 4. So you take 3 out of those 4, and compare them with 3 normal coins (2nd step). If they still balance, then the different coin is the other one, and you can compare it with a normal one to see if it is heavier or lighter (3rd step). If they don't balance anymore, then the coin is among those 3. Since you can see if it is heavier or lighter looking at the position of the plate (up or down), you just need to find the heavier or lighter one among 3 in one step, and it's simple (3rd step).

If they don't balance... heh, this is difficult to explain. The coin is among those 8. One plate is up, the other is down. If the different coin is on the high plate, then it is lighter, if it is on the low plate, then it is heavier. Now replace 3 of the 4 on the high plate with 3 of the 4 on the low plate, and replace those 3 on the low plate with 3 normal ones (2nd step). What happens?
- If nothing happens, that means the coin is one of the 2 you didn't replace (either a lighter one on the high plate or a heavier one on the low plate). You compare one of them with a normal one and you'll find what's the diifferent one and if it is heavier or lighter. (3rd step)
- If they balance, that means you took away the different one from the plates. You took away 3 coins from the high plate, so the different coin is actually lighter and among those 3. It is simple to find the lighter one among 3 in one step (3rd step).
- If the high plate goes down, you now have a plate down (with 4 coins, one was supposed to be lighter and 3 were supposed to be heavier, considering the previous step), and a plate up (with 3 normal coins and one coin that was supposed to be heavier, considering the previous step). The only thing that makes sense is that there is a heavier coin among the 3 you moved from one plate to another. So now you can find the heavier one among three with just one more step (3rd step).

Well, that was kind of difficult! And expressing that in written English... that was difficult too!

Math? Well, yeah, but not pure math. But I really don't know much about math.
Anyway, that stuff didn't have much to do with math, I think. It was more like logic and intuition.