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1. If X people are transferred to the library, then 15-x people will go to the laboratory.

There are 2 1+x people in the library and 12+ 15-x = 27-x people in the laboratory.

Make the library twice as big as the laboratory, 2 1+x = 2*(27-x), and get x = 1 1.

Then transfer to 1 1 person.

2. If there are four people left, then assign 1 1 person and transfer x people to the library, then 1 1-x people go to the laboratory.

There are 2 1+x people in the library and12+11-x = 23-x people in the laboratory.

The number of people in the library is twice that of the laboratory, 2 1+x = 2 *(23-x), and x ≈ 8.33 people.

Then at least nine people have been assigned to the library, so there is less 1 person, so it can't be assigned by the monitor.