Logical Analysis and reasoning (find out the problem of light ball)

Problem:

There are 12 balls with the same appearance, one of which has different weights (Here we assume it is lighter) (or it does not indicate lighter or heavier), giving you a scale-free balance, you can only use it three times. How can you find the light ball?

 

Problem Analysis:

I. First, it is clear that the ball is light.

Method 1

(1) At, we got a bunch of lighter results,

(2) then put a bunch of Light points at to get a bunch of Light points,

(3) place any two of them in a light pile on the balance,

Judging, if the balance is balanced, the light ball is not put, and if the balance is not balanced, the high side is light ball.

Method 2

(1) divide the ball into three heaps:, which is called any two heaps. If the balance is reached, the remaining heap is light. If the balance is not balanced, the heap is light,

(2) put a light heap of balls at and get a light heap,

(3) Get a light ball on one side of the heap.

2. It does not indicate whether it is a light ball or a heavy ball (I have to find it four times. I don't know if I have any expert tips)

Method 1

Divide the ball into three parts: A, B, C, and D.

(1) If a and B are balanced,

(2) then A and C are called. If the balance is D (marked as Case 1 ),

If it is not balanced, it is C, And you know whether the ball is light or heavy (marked as case 2 ).

 

In Case 2, (3) You can name any two balls in heap C and determine which ball is different,

 

In Case 1, the D heap is divided into D1, D2, and D3,

(3) Then D1 and D2 are called, (4) D1 and D3 are called, and different balls are determined.

Method 2

Divide the ball into three heaps:, marked as A, B, and C, respectively,

(1) a B,

(2) a c said, judge to get a bunch of different, and know whether it is a light ball or a heavy ball

(3) place a different heap of balls at 2: 2 and get another heap,

(4) Get a different ball on one side of the last heap.