Interesting question--12 coins problem

Problem Description:

12 gold coins, one of which is fake and the weight is different. The existing balance requires you to weigh the fewest number of times and then tell me:

(1) which gold coin is false

(2) Whether it is lighter or heavier.

(Note: Here are 3 times)

Fill in the picture abstract (optional)

{ explanation of problem solving:

The first step: one side 4, if the balance is flat, counterfeit money in the remaining 4, or in the balance of 8. Now divide the situation 1: in 4 in: Between the balance on one side 1, so no matter what kind of situation to be excluded is left 2, holding two and standard (that is, you have ruled out a certain) better than the situation

2: In 8 of the balance, here is a key point: the weight of the ball every time that the side will be heavy, light ball every time the side will be light , so sometimes light and sometimes heavy must be ordinary to the 8 balls to make a number, a heavy group called 1 2 3 4, the light group called 5 6 7 8, and 4 normal balls are called X good.

Note Here I got two workarounds and don't rule out a third, fourth, or more:

Method 1:

1. Balance 1XXX on the left and 2348 on the right.

2.1 If the left side is still heavier than the right side, we can know that 1 and 8 is a problem, but do not know whether the counterfeit currency is lighter or heavier (because 234 does not exist in the effect of the impact factor, XXX is normal)

2.2 If there are two sides of the same weight, we can conclude that the problem is (5,6,7), by the condition of the known condition 2 can know that the problem of counterfeit money should be lighter, it is easy to use a weighing in the 5,6,7 to find the counterfeit currency! --ex:5 left 6 right, oblique words light is false, flat words 7 is false.

(Method 1 This paragraph is my personal description)?

Method 2:

We left 1 2 5, the right side of the 3 6 X, the remaining 4 7 8 do not put up, assuming that the balance is flat, then 4 7 8, said 78, flat means 4 is heavy, uneven who light is who now look at the balance of the situation: if 1 2 5, then the candidate ball is 1 2 6, and the above similar, said 12 can. If 1 2 5 light, then the candidate ball is 3 5, two balls casually and the standard ball than a bit better

Finished solving the problem}?

?

After that I got some information through the search, about this problem abroad people have sent paper, with the knowledge of information theory to explain and do the promotion.

Later I went to the library to borrow the "information base"-the two authors of the United States books, read, and found that the information theory is very different from what I imagined, I would like to be able to use information theory to help me master some philosophical principles to guide life (well, that's true! ~ ~ ~ It can be found at this time that the theory of information involves a lot of mathematical principles, the requirements of mathematics is higher , at present more is to be used in coding work, which for communications engineering people are still very helpful. Some reading soon proved that they were not interested.

At last:

If you are interested in 12coins problems and want to get some inspiration, I recommend this article, I believe you can open up your mind:

similar question: N table tennis has one and other quality different, with the balance at least a few times must be able to weigh out? Discussion

Just the sauce:)

Interesting question--12 coins problem