A smart question: there are 12 table tennis balls, one of which is out of specification, but I do not know whether it is light or heavy. It is required that the ball be identified three times in Tianping.

Question:

There are 12 table tennis balls, one of which is out of specification, but I do not know whether it is light or heavy. It is required that the ball be identified three times in Tianping.

 

Method:

Each ball is marked with a number ranging from 1 to 12.

1 2 3 4 vs 5 6 7 8
There will be three possibilities
①, 1 2 3 4> 5 6 7 8
②, 1 2 3 4 = 5 6 7 8
③, 1 2 3 4 <5 6 7 8

2 5 8 11 vs 3 6 9 12
A, 2 5 8 11> 3 6 9 12
B, 2 5 8 11 = 3 6 9 12
C, 2 5 8 11 <3 6 9 12

The third term is:
1). ① and a are inferred as follows:
1 2 3 4> 5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11> 3 6 9 12 => 1 4 7 10 is a good ball
3, 5, 8 changed the position, but the balance direction did not change, SO 3, 5, 8 is a normal ball
So there is a bad ball in 2 and 6, and 2> 6
Place 2 and other known good balls (such as 12) on the second side of the balance. The results are as follows:
If 2> 12, 2 is a bad ball (heavy)
If 2 = 12, 6 is a bad ball (light)
If 2 <12, this situation does not occur, otherwise it is inconsistent with the meaning of the question (6 <2 <12)

2). ① and B are inferred as follows:
1 2 3 4> 5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11 = 3 6 9 12 => 2 5 8 11 3 6 9 12 is a good ball, and 1 4 7 is a bad ball.
1 + 4> 5 (Good ball) + 7
7 indicates a bad ball (light), or 1 or 4 indicates a bad ball (heavy)
Place 1 and 4 on the Tianping 2, respectively. The results are as follows:
If 1> 4, 1 is a bad ball (heavy)
If 1 = 4, 7 is a bad ball (light)
If 1 is less than 4, 4 is a bad ball (heavy)

3). ① and C are inferred as follows:
1 2 3 4> 5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11 <3 6 9 12 => 1 4 7 10 is a good ball
Similarly, 2 6 is a good ball, and 3 + 6 (Good ball)> 5 + 8
It is inferred that 3 is a bad ball (heavy), or 5 or 8 contains a bad ball (light)
Place 5 and 8 on the 2 ends of the balance, respectively. The results are as follows:
If 5> 8, 8 is a bad ball (light)
If 5 = 8, 3 is a bad ball (heavy)
If 5 is <8, 5 is a bad ball (light)

4). ② the speculation of a is as follows:
1 2 3 4 = 5 6 7 8 => 1 2 3 4 5 6 7 8 is a good ball and 9 11 12 is a bad ball.
2 5 8 11> 3 6 9 12 => 1 4 7 10 is a good ball
2 (Good ball) + 11> 9 + 12
It is inferred that 11 is a bad ball (heavy), or 9 or 12 contains a bad ball (light)
Place 9 and 12 on the 2 ends of the balance, respectively. The results are as follows:
If 9> 12, 12 is a bad ball (light)
If 9 = 12, 11 is a bad ball (heavy)
If 9 is <12, 9 is a bad ball (light)

(5) ② and B are inferred as follows:
1 2 3 4 = 5 6 7 8 => 1 2 3 4 5 6 7 8 for good balls
2 5 8 11 = 3 6 9 12 => 2 5 8 11 3 6 9 12 for good balls
We can see that 10 balls are bad balls. If you need to know the weight, you can
Place 10 and 12 on the 2 ends of the balance, respectively. The results are as follows:
If 10> 12, 10 is a bad ball (heavy)
If 9 = 12, it is impossible
If 10 is less than 12, 10 is a bad ball (light)

6). ② and C are inferred as follows:
1 2 3 4 = 5 6 7 8 => 1 2 3 4 5 6 7 8 is a good ball and 9 11 12 is a bad ball.
2 5 8 11 <3 6 9 12 => 1 4 7 10 is a good ball,
2 (Good ball) + 11 <9 + 12
It is inferred that 11 is a bad ball (light), or 9 or 12 contains a bad ball (heavy)
Place 9 and 12 on the 2 ends of the balance, respectively. The results are as follows:
If 9> 12, 9 is a bad ball (heavy)
If 9 = 12, 11 is a bad ball (light)
If 9 is <12, 12 is a bad ball (heavy)

7). ③ The situation of A is estimated as follows:
1 2 3 4 <5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11> 3 6 9 12 => 1 4 7 10 is a good ball
Similarly, we can infer that 2 and 6 are good balls.
1 (Good ball) + 3 <5 + 8
It is inferred that 3 is a bad ball (light), or 5 or 8 contains a bad ball (heavy)
Place 5 and 8 on the 2 ends of the balance, respectively. The results are as follows:
If 5> 8, 5 is a bad ball (heavy)
If 5 = 8, 3 is a bad ball (light)
If 5 is <8, 8 is a bad ball (heavy)

(8) ③ and B are inferred as follows:
1 2 3 4 <5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11 = 3 6 9 12 => 2 5 8 11 3 6 9 12 is a good ball, and 1 4 7 is a bad ball.
1 + 4 <5 (Good ball) + 7
It is inferred that 7 is a bad ball (heavy), or 1 and 4 have a bad ball (light)
Place 1 and 4 on the Tianping 2, respectively. The results are as follows:
If 1> 4, 4 is a bad ball (light)
If 1 = 4, 7 is a bad ball (heavy)
If 1 is less than 4, 1 is a bad ball (light)

9) ③ and C are inferred as follows:
1 2 3 4 <5 6 7 8 => 9 10 11 12 is a good ball
2 5 8 11 <3 6 9 12 => 1 4 7 10 is a good ball
Similarly, 5 8 3 is a good ball.
2 <6
It can be seen that 2 is a bad ball (light) or 6 is a bad ball (heavy)
Place 2 and other known good balls (such as 12) on the second side of the balance. The results are as follows:
If 2> 12, this situation does not occur, otherwise it is inconsistent with the meaning of the question (12 <2 <6)
If 2 = 12, 6 is a bad ball (heavy)
If 2 is less than 12, 2 is a bad ball (light)