Off >> on, odd number

9* odd number = odd number

6* any = even number

So it's impossible

2 yes:

No. 12345678

First pull 1234567, no pull 8.

Don't pull 1

Don't pull for the third time.

....

Don't pull 7 for the eighth time.

Pull each lamp seven times and turn it on. This is the easiest way.

The 25th thought of the above answer.

Now, on the 27th, I went back to study and found more things:

Question: M lights, N lights at a time, can they all be on?

Solution:

1. If n is odd, ok. The method is to pull the first n lamps first, and then the second lamp, ..... so that a total of M*N lamps are pulled, so each lamp is pulled n times, and n is an odd number. Open.

For example, if you switch three lights to five lights at a time, you can switch 123, 234, 345, 45 1, 5 12.

This method is the simplest only when m and n are coprime, but it must be feasible!

2. If m is odd and n is even, it is not, which is explained in the original problem.

3. If m is even and n is even, OK. Dislocation, two lights on at the same time:

For example, six lights, four lights at a time. First, turn on 12, and any other 4- 1=3 lights as temporary (take 345 here). If you turn on1345,2345, then turn on 12, and the other lights will remain unchanged. Because m is an even number, two lights will be turned on at a time.

This method is basically not the simplest, but it must be feasible.