There are eight teacups on the table. All the cups are facing up, four at a time, and they are all facing down as long as they are turned twice.

If you change eight questions into six, and turn over four at a time, can you turn them all down after several turns?

Please try it, and then you will find that you can achieve your goal by flipping it three times. The explanation is as follows:

With 1, the cup mouth is up,-1, and the cup mouth is down. These three turning processes can be simply expressed as follows.

Initial state +l, +l, +l, +l, +l, +l,+l.

Turn-1,-1,-1, -l, +l,+1 first.

Second flip+1,+1,+1,+1,-1.

The third flip -l, -l,-1, -l, -l,-1.

If you change the 8 blocks in the question into 7 blocks, can you turn them all down several times (4 blocks at a time)?

After several experiments, you will find that you can't turn them all into cups with your mouth facing down.

Is your "flip" ability poor, or can't finish it at all?

"1" will tell you that no matter how many times you turn it over, you can't let these seven cups face down.

There is a simple reason. If you use 1 to indicate that the cup mouth is up and-1 to indicate that the cup mouth is down, the question becomes: "If you change the symbols of four of the seven 1 at a time, can you change them all to-1 after several times?" Considering the product of these seven numbers, because the sign of four numbers changes every time, their product will never change (that is, it will always be+1), and when all the cups are facing down, the product of seven numbers is equal to-1, which is impossible.