Marked mathematics - Training Enrollment Network

Marked mathematics

Weigh the mass of eight balls with a balance. If one ball is heavier than the other seven balls, you can find the heavy ball.

The specific operation process is as follows:

1. Marking: Mark eight balls with 1, 2, 3, 4, 5, 6, 7 and 8 respectively.

2. Grouping: Divide the eight marker balls into three groups, 1, 2,3 in group A, 4,5,6 in group B and 7,8 in group C. ..

3. Operation:

(1) First weighing: Put group A balls and group B balls on the left and right sides of the balance respectively, and there will be three situations:

(I) Case 1: A = B, which means that six balls have the same mass, and the heavy ball is in Group C. ..

(2) the second case: A > B, which means that three balls in group a have heavy balls.

For the second weighing, put the 1 ball and the No.2 ball on both sides of the balance respectively, and there will be three more situations:

(a) Ball 1 and Ball 2 have the same mass, indicating that Ball 3 is a heavy ball;

(b) The mass of ball 1 is greater than that of ball 2, which means that ball 1 is a heavy ball;

(3) The third case: A < B means that the ball in Group B has a heavy ball.

The second weighing, put the No.4 ball and No.5 ball on both sides of the balance respectively, and there will be three situations:

(a) Ball No.4 and Ball No.5 have the same mass, indicating that Ball No.6 is a heavy ball;

(b) The mass of the No.4 ball is greater than that of the No.5 ball, indicating that the No.4 ball is a heavy ball;

(2) When weighing for the first time, the first situation appears, that is, A = B. When the heavy ball is in Group C,

Weigh the 7th and 8th balls on both sides of the balance respectively, and there will be two situations:

(i) The mass of No.7 ball is greater than that of No.8 ball, indicating that No.7 ball is a heavy ball;

(2) The mass of No.8 ball is greater than that of 1, which means that No.8 ball is a heavy ball.

In short, the heavy ball can be found at least twice and at most three times.