28 hotel rooms

There are three schemes: (1) 1 small room +4 large rooms; (2)4 small rooms +2 large rooms; (3)7 small rooms

Suppose a small room needs x rooms, and a large room needs y rooms, and 28 people can live in it.

Then: 4X+6Y=28, then: Y=(28-4X)/6.

When X= 1, Y=(28-4* 1)/6=4.

When X=2, Y=(28-4*2)/6=3.333, this situation is removed because every room is full;

When X=3, Y=(28-4*3)/6=2.666, remove as above;

When X=4, y = (28-4 * 4)/6 = 2;

When X=5 and Y=(28-4*5)/6= 1.333, this situation is removed;

When X=6, Y=(28-4*6)/6=0.666, this situation is removed;

When X=7, Y=(28-4*7)/6=0.

From this, we can draw the above three schemes.