Math Problems, Genius Progress????

First, divide the 12 balls into three parts: 4:4:4, and set them to three piles of A, B, and C.

1。If A=B, then, the defective product is in C, and then choose any 3 from C, and compare it with the 3 ** balls in A or B, then, 1) If it is equal, then the remaining ball is a defective product, and then compare it with the ** ball to know.

Is it light or heavy.

2) If it is not equal, then there are two more cases.

1] C(3)> Positive (3), then the defective product is in C(3), and it is heavier than **ball, so it is from C(3).

Choose any two to compare, a) if they are equal, then the remaining one is a defective product, and the defective product is heavier.

b) If it is not equal, the heavier one is inferior.

2] c(3) "positive (3), then the defective product is also in c(3), and it is lighter than **ball, so it is from c(3).

Pick two to compare, a) if they are equal, then the remaining one is a defective ball and the defective is lighter.

b) If it is not equal, the lighter one is a defective ball.

2。If A is not equal to B, then there must be a heap of light and a heap of heaviness, and we might as well think of the heavier heap as a (it's just.

For the sake of convenience, it doesn't really matter), and the lighter pile is considered b. Then divide A into 1+3 parts.

Don't write it down as a(1) and a(3), divide b into 2+2 parts, write it as b(2) and b (2) respectively, and compare a(3)+

The weight of b(2) and a(1) + positive (3), then there are three cases: (Note: because A is heavier than B, the ball in A.)

The weight of the ball must be greater than or equal to the weight of the ball, which is a very important implicit condition, otherwise the problem cannot be solved).

1) a(3)+b(2)=a(1)+positive (3), then the defective product must be in b (2), and the weight is lighter, so it is than.

Compare the two balls in b (2), the lighter one is defective.

2) A(3)+B(2)>A(1)+Positive (3), because the weight of the ball in A is at least equal to the **ball, so the defective product is certain.

In a(3), and the weight is heavier than the ** ball, then choose two balls from a(3) to compare, 1] if equal, then the remaining one is defective, and heavier;

2] If it is not equal, the heavier one is defective.

3) a(3)+b(2)< a(1)+positive (3), the situation is more complicated, there are two possibilities, or a(1) is defective and.

Heavier than **, or there is a defective product in b(2) and it is lighter than **, so just compare the two in b(2).

The weight of the ball, you can make a judgment:

1] If the two balls in b(2) are equal, then the two balls must be **, then the defective is must be.

a(1), and heavier than **.

2] If the two balls in b(2) are not equal, the lighter one is inferior.

It's much easier to know if it's heavier or lighter.

I'll tell you about the bonus points of 100!

The answer is as follows:

You can ask others for questions that you don't know, but the purpose should not only be to know the answer, but more importantly, to learn how to solve the problem and understand the problem, otherwise you will lose the meaning of learning. The purpose of assignments and tests is to check whether the knowledge has been learned and to reinforce and retain the knowledge.

The help of others can only be temporary, and learning by yourself is eternal.