If 12 balls are woven into numbers 1, 2... 12, the following symbols can be designed:
Left disk * * * Right disk
First time 1, 5,6,12 * * 2, 3,7, 1 1
Second 2, 4, 6,10 * *1,3, 8, 12
The third 3,4,5,11* *1,2,9, 10.
There may be three results every time: flat, left weight and right weight, and there are 27 results when matching, but the results of flat, flat and flat will not appear, because there is always a ball that is not equal. Similarly, the results of left, left, left, right, right and right will not appear again, because according to the designed notation, there is no ball left or right three times. The remaining 24 results show which situation is which ball. For example, if the result is flat, flat, left or flat and right, you can judge that it is the No.9 ball, because there is no No.9 ball in the first and second time, but there is a No.9 ball in the third time, and both the first and second times are flat, only the third time is unbalanced, which shows that the weight of No.9 ball is different from other balls. According to this principle, we can judge which ball is the other case.
There are 12 balls, and the bad ball may be lighter than the good ball or heavier than the good ball, so there are * * *, 12x2=24 possibilities, and the 24 possible results are as follows:
************ ********** ************ **********
* can *-* blossom and bear fruit * * can *-* blossom and bear fruit *
************ ********** ************ **********
Ball 1, weight-left, right, right ball 1, weight-right, left, left.
The second ball, and the second ball with heavy right, left and right, and the light left, right and left.
Ball number three, heavy-right, right, left ball number three, light-left, left, right.
The fourth ball, and the heavy flat, left and left four balls, and the light flat, right and right.
The No.5 ball is heavy left and flat left, light right and flat right.
The No.6 ball is heavy left and flat left, light right and flat right.
The no.7 ball is flat on the right and flat on the left.
No.8 ball, heavy flat, right flat, No.8 ball, light flat, left flat.
No.9 ball, and the heavy flat, flat and right No.9 ball, and the light flat, flat and left.
Ball 10, and balance, left and right ball 10, and light balance, left and right.
1 1 ball, 1 1 ball is heavy on the right and flat on the left, but light on the left and right.
The weight of the ball 12 is flat, and the weight is flat.
None of the above 24 results are repeated, and the above results can be regarded as possible reverse push, or the only ball can be introduced as a bad ball, which proves that this method is feasible.
The second answer
There are 12 balls and a balance. Now we know that only one of them is different in weight from the others. How can we find the ball after weighing it three times? Note that this problem does not indicate whether the weight of the ball is light or heavy, so it needs careful consideration. )
Reference answer 1:
First, divide the ball of 12 into three equal parts, each with four balls.
Take out two and weigh them on both sides of the balance (for the first time)
Situation 1: The balance is balanced.
Then the eight balls are all normal, and the special ones are four.
Take out three of the remaining four balls and put them aside, and put three normal balls on the other side (the second time)
If it is balanced, what is special is the remaining one.
If it is not balanced, it is in three boxes above the balance. And know whether it is heavy or light.
Take two of the remaining three and weigh them. Because we already know the weight, we can know the special one. (the third time)
Case 2: Balance tilt.
The special ball is at one eighth of the balance.
Write the four balls on the heavy side as A 1A2A3A4, and the light ones as B 1B2B3B4.
The rest are determined to be four normal, marked C.
Put A 1B2B3B4 aside, and B 1 and three normal c balls aside. (second time)
Situation 1: The balance is balanced.
The special ball is in A2A3A4, and I know that the special ball is heavier.
Weigh A2A3 and you will know which of the three is more special. (the third time)
Case 2: the balance is still A 1, which is relatively heavy.
The special ball is between A 1 and B 1.
Just take an ordinary scale and you will know which one is special. (the third time)
Situation 3: On the other hand, the balance is heavier at B 1
The special ball is in the middle of B2B3B4, and it is known that the special ball is lighter.
Weigh B2B3 and you'll know which one is special. (the third time)
Reference answer 2:
This method is to make sure to find the bad ball three times and know whether it is heavier or lighter than the standard ball.
Number the twelve balls as 1- 12.
For the first time, put 1-4 on the left and 5-8 on the right.
1. If the weight is right, the bad ball is in 1-8.
Remove No.2-4 for the second time, move No.6-8 from right to left, and put No.9-11.
It's on the right. That is to say, put 1, 6, 7, 8 on the left and 5, 9, 10,1/on the right.
1. If the weight, the bad ball in the untouched 1, 5. If it is 1,
It is lighter than the standard ball; If it's a No.5 ball, it's heavier than the standard ball.
Put 1 on the left and No.2 on the right for the third time.
1. If the weight is appropriate, 1 is a bad ball, which is lighter than the standard ball;
2. If it is balanced, the 5th ball is a bad ball, which is heavier than the standard ball;
It can't be left-handed this time.
2. If it is balanced, the bad ball is lighter than the standard ball in the number 2-4 that has been removed.
Put No.2 on the left and No.3 on the right for the third time.
1. If the weight is appropriate, the No.2 ball is a bad ball, which is lighter than the standard ball;
2. If it is balanced, the No.4 ball is a bad ball and lighter than the standard ball;
3. If the left is heavy, No.3 is a bad ball, which is lighter than the standard ball.
3. If the left ball is heavy, the bad ball will be taken to the left 6-8, which is heavier than the standard ball.
For the third time, put No.6 on the left and No.7 on the right.
1. If the weight is appropriate, No.7 is a bad ball, which is heavier than the standard ball;
2. If it is balanced, the No.8 ball is a bad ball and heavier than the standard ball;
3. If the left ball is heavy, No.6 is a bad ball, which is heavier than the standard ball.
2. If the balance is balanced, the bad ball is 9- 12.
The second time, put 1-3 on the left and 9- 1 1 on the right.
1. If the weight is appropriate, the bad ball is 9- 1 1, and the bad ball is heavier.
Put No.9 on the left and 10 on the right for the third time.
1. If the weight is appropriate, 10 is a bad ball, which is heavier than the standard ball;
2. If it is balanced, the number 1 1 is a bad ball, which is heavier than the standard ball;
3. If the left ball is heavy, No.9 is a bad ball, which is heavier than the standard ball.
2. If it is balanced, the bad ball is 12.
For the third time, put 1 on the left and 12 on the right.
1. If the weight is appropriate, 12 is a bad ball, which is heavier than the standard ball;
2. It is impossible to balance at this time;
3. If the left ball is heavy, the number 12 is a bad ball, which is lighter than the standard ball.
3. If the left is heavy, the bad ball is 9- 1 1, and the bad ball is lighter.
Put No.9 on the left and 10 on the right for the third time.
1. If the weight is appropriate, the No.9 ball is a bad ball, which is lighter than the standard ball;
2. If it is a balance ball, the number 1 1 is a bad ball, which is lighter than the standard ball;
3. If the left ball is heavy, 10 is a bad ball, which is lighter than the standard ball.
3. If the left is heavy, the bad ball is in 1-8.
Remove No.2-4 for the second time, move No.6-8 from right to left, and put No.9-11.
It's on the right. That is to say, put 1, 6, 7, 8 on the left and 5, 9, 10,1/on the right.
1. If the right ball is heavy, the bad ball will be taken to the left 6-8, which is lighter than the standard ball.
For the third time, put No.6 on the left and No.7 on the right.
1. If the weight is appropriate, No.6 is a bad ball, which is lighter than the standard ball;
2. If it is a balance ball, the No.8 ball is a bad ball, which is lighter than the standard ball;
3. If the left is heavy, No.7 is a bad ball, which is lighter than the standard ball.
2. If it is balanced, the bad ball is heavier than the standard ball in the number 2-4 that has been removed.
Put No.2 on the left and No.3 on the right for the third time.
1. If the weight is appropriate, the No.3 ball is a bad ball, which is heavier than the standard ball;
2. If it is balanced, No.4 is a bad ball, which is heavier than the standard ball;
3. If the left ball is heavy, No.2 is a bad ball, which is heavier than the standard ball.
3. If the left is heavy, the bad ball is at the untouched number 1, 5. If it is 1,
It is heavier than the standard ball; If it's a No.5 ball, it's lighter than the standard ball.
Put 1 on the left and No.2 on the right for the third time.
1. It can't be right this time.
2. If it is balanced, the No.5 ball is a bad ball and lighter than the standard ball;
3. If the left ball is heavy, the number 1 is a bad ball, which is heavier than the standard ball;
Reference answer 3:
|-Right -( 1 light)
|-right-(1; 2)|- Flat -(5 times)
||||-Left-()
|
||||-Right -(2 lights)
|-right -( 1, 6-8; |-Ping-(2; 3)|- Plane -(4 light)
| 5,9-11) ||-left -(3 lights)
| |
|||||-Right-(30% off)
||||-Left-(6; 7)|- Ping-(20% off)
||||-Left -(6 times)
|
||||-Right -( 10 weight)
||||-Right-(9; 10)|- Ping -( 1 1 weight)
|||||-Left-(10% off)
| |
||||-Right -( 12 weight)
( 1-4; 5-8)|- Ping-(1-3; |-Ping-(1; 12)|- Ping -( 13 light, 13 heavy) *
| 9- 1 1)| |- left -( 12 light)
| |
|||||-Right -(9 lights)
||||-Left-(9; 10)|- flat -( 1 1 bright)
||||-Left -( 10 light)
|
||||-Right -(6 lights)
||||-Right-(6; 7)|- Flat -(8 light)
|||||-Left -(7 lights)
| |
|||||-Right-(three times)
|-Left -( 1, 6-8; |-Ping-(2; 3)|- Ping-(quadrupling)
5,9-11) ||-left -(2 times)
|
||||-Right-()
|-Left-(1; 2)|- Plane -(5 light)
|-Left -( 1 weight)
I don't know which one you want