2 ~ 3 items, call 1 time.

4 ~ 9 items, representing 2 times.

10 ~ 27 items, representing 3 times.

28 ~ 8 1 item, representing 4 times.

The above is to know the severity of the defective products, but it is more important to say that the defective products are light. The law should be 3 to the power of n, and n is the number of times needed. According to n times, you can distinguish the n power of 3 at most.

Extended data:

Example:

There are 12 coins, and the weight of one coin is different from the others. Three times, we used the opportunity of measuring the balance to find out the one with different weight.

Solution: code 12 coin 1~ 12. Divide coins into three groups:

A: 1, 2, 3, 4

B: Five, six, seven, eight.

C: 9, 10, 1 1, 12.

First weighing:

A = B. Then the special coins are in Group C, and the normal coins of A and B can be used as a reference.

Second weighing:

Normal coins 5 and 6 and 9 and 10. There will be two situations:

If they are equal, the special currency is 1 1 and 12.

The third weighing:

Compare 10 and 1 1. If they are equal, 12 is a special coin (the weight is unknown); If not, 1 1 is a special coin.

If not, the special coin is at 9, 10 (depending on the weight).

The fourth weighing:

Comparing 8 with 9 means that 10 is a special coin. Unequal means that 9 is a special coin. A and B are not equal (one weight), which means that Group C is a normal coin. Let the coins in A be a 1, a2, a3, a4 (if there are defective products, the defective products are definitely more important than the genuine products); The coins in B are b 1, b2, b3, b4 (if there are defective products, they must be lighter than the genuine ones).

Take a coin from C and divide it into three groups with A and B:

D:a 1、a2、c

E:a3、a4、b 1

Female: b2, b3, b4

Second weighing: weigh d and e.

1, D=E, indicating that the special currency is in F, which is lighter.

Third Weighing: Compare b2 and b3: If they are equal, b4 is a special coin; if not, it is a lighter coin.

2.d is more important than E, so either a 1 and a2 are heavier (that is, the defective products are heavier) or b 1 is lighter.

Third weighing: compare a 1 and a2. Equal means that b 1 is a lighter special coin, and unequal means a heavier special coin.

D is lighter than E, which means that a3 and a4 have a particularly heavy coin.

Fourth weighing: Compare a3 and a4. The heavier ones are special coins.