12 Table Tennis

Continue Simple puzzles:

There are 12 table tennis, one of which is defective, defective and normal table tennis appearance is the same, only the weight is different, may be lighter than normal, may be heavier than normal, there is now a balance, 3 times to weigh the defective method.

Now think of the answer:

For the convenience of instructions, table tennis is numbered according to 1-12.

In the first step, the table tennis is divided into 3 groups, each group of 4, for example (1,2,3,4), (5,6,7,8), (9,10,11,12), the first group and the second group put up to say, there may be 3 results: The 1th group is heavier, balanced, and the 2nd group is more heavy.

Look at the simple case first, if the balance, then the 1th and 2nd Group of 8 table tennis is normal, the defective must be in the 3rd Group of 4 table tennis, then the next 2 is relatively simple, from the 3rd group to take 2 (9,10), and then from the 1th Group and the 2nd group also take 2 (8 is normal, Suppose go to 1 and 2), respectively placed on the balance of the left and right 2 sides, if the balance, then the defective goods must be in the remaining 11 and 12, if unbalanced, then the defective must be in 9 and 10. The last time as long as from 2 to take one, and a normal comparison, if the balance, then the remaining one is defective, if not balanced, then the one that was taken out is defective.

Now look at the first unbalanced situation, assuming that the 1th group is heavier (the same is true for the 2nd group). First of all, the rest of the (9,10,11,12) 4 is certainly normal. 2nd, the left with 9,10,11 to replace the first, then the 4 and 5 exchange, called once. That is, the balance to the left is (5,9,10,11), the balance to the right is (4,6,7,8). There are also 3 kinds of situations: the left is heavy, just balanced, right.

discussed separately, (1) If the right weight, then the defective is certainly in the exchange of 4 and 5 in the middle of a, the last said as long as the 4 and a normal comparison, you can determine whether 4 is defective or 5 is defective. (2) If the left is heavy, that 4 and 5 are normal, because the left 9,10,11 in the first call in the judgment is normal, then the defective is certainly in the right side of the 6,7,8. And the defective is certainly lighter than normal (this judgment is very important), because the Left 4 is normal, the right 3 only normal plus a defective, left heavy, then the defective must be light. 3rd said that as long as the 6 and 7 are weighed once, the light that is defective, if balanced, then 8 is defective. (3) If it is balanced, then the defective is the top is replaced by one of the two, and the defective is definitely biased, reasoning defective reason is the first name is left, defective on the left. If the 3rd is called, then the defective can be found in the.

In fact, the key is to seize if you know the defective is light or biased, then only 1 said can be in 3 alternatives to judge the defective, otherwise, 1 said at most can only be in 2 alternatives to determine the defective.

12 Table Tennis