12 balls, one is different from the others, provide a balance, find out three times

12 balls, one is different from the others, provide a balance, find out three times

Divided into 3 piles and marked as: A1 A2 A3 A4 and B1 B2 B3 B4 and C1 C2 C3 C4

Compare A1 A2 A3 A4 with B1 B2 B3 B4 for the first time

• If the balance is balanced, it means that the problematic ball is in C1 C2 C3 C4

  • Then compare A1 A2 A3 with C1 C2 C3
    • If the balance is balanced, it means that there is a problem with C4
      • The third time: Take another small ball and compare it with C4, and you can conclude whether C4 is light or heavy
    • If the balance is not balanced, then the problem ball is in C1 C2 C3, because A1 A2 A3 is a standard ball, now we know whether the problem ball is light or heavy
      • The third time: compare with C1 and C2
        • If the balance is balanced, then there is something wrong with C3, and the weight of C3 can be known according to the second comparison result
        • If the balance is not balanced, the result can be obtained according to the second judgment. If the second time is that the ball is lighter, then there is a problem with the lightness (and vice versa)

• The imbalance indicates that the problem ball is in A1 A2 A3 A4 or B1 B2 B3 B4. The following two situations are discussed

  • front heavy back light
    • Compare A1 A2 B1 with A3 A4 B2 for the second time
      • if balance
        • For the third time, take a normal ball and compare it with B3
          • If the balance is unbalanced, B3 is the problem ball, and it will only be that B3 is lighter (because the front is lighter than the back, if B3 is heavy, the front will be lighter and the back is heavier)
          • If the balance is balanced, B4 is the problem ball, and B4 is lighter (because the back is lighter when compared with the front)
      • If it is unbalanced, it means that the problem ball is in A1 A2 B1 or A3 A4 B2. The following two situations are discussed
        • If the second time is still heavy in the front and light in the back , it means that A1 and A2 are heavy, or B2 is light (because the first value is heavy in the front and light in the back, it means that the exchanged ball has no effect on the balance of the balance, that is, the original ball has a problem)
          • The third time: weigh A1 A2
            • If the balance is balanced, it means that there is a problem with B2.
            • If the balance is out of balance, there is something wrong with the heavy one, it is too heavy
        • If the second time is that the front is light and the back is heavy , it means that A3 and A4 are heavy, or B1 is light (when the order is changed, the balance of the balance has changed, indicating that the problem ball is in the exchanged ball)
          • The third time: weigh A3 A4
            • If the balance is balanced, it means that there is a problem with B1.
            • If the balance is out of balance, there is something wrong with the heavy one, it is too heavy
  • Light in front and heavy in back (light ball in A, or heavy ball in B)
    • Compare A1 A2 B1 with A3 A4 B2 for the second time
      • If it is balanced, it means that the problem ball is in B3 or B4
        • For the third time, take a normal ball and compare it with B3
          • If the balance is not balanced, B3 is the problem ball, and only B3 is heavier (because the front is heavier than the back, if B3 is lighter, the front will be heavier than the back)
          • If the balance is balanced, B4 is the problem ball, and B4 is heavier (because the back is heavier when compared with the front)
      • If it is unbalanced, it means that the problem ball is in A1 A2 B1 or A3 A4 B2. The following two situations are discussed
        • If the second time is still light in the front and heavy in the back , it means that A1 and A2 are lighter, or B2 is heavier (because the first value is light in the front and heavier in the back, it means that the exchanged ball has no effect on the balance of the balance, that is, the original ball has a problem)
          • The third time: weigh A1 A2
            • If the balance is balanced, then there is something wrong with B2 and it is heavy
            • If the balance is not balanced, there is a problem with the lighter one, the lighter
        • If the second time is that the front is heavy and the back is light , it means that A3 and A4 are lighter, or B1 is heavier (after the ball is exchanged, the balance of the balance has changed, indicating that the problem ball is in the exchanged ball)
          • The third time: weigh A3 A4
            • If the balance is balanced, then there is something wrong with B1, it is heavy
            • If the balance is not balanced, there is a problem with the lighter one, the lighter