There are 23 people in the tour group staying in the hotel, living in three rooms and two halls (no empty beds in each room). How many different arrangements are there? Please list and explain.

There are four different arrangements.

X has three rooms and Y has two rooms. According to the meaning of the question, we can get the equation:

3x+2y=23，

The equation can be transformed into: y=(23-3x)/2.

Because both x and y are integers, in order to ensure that the value of y is an integer, the value of 23-3x must be an even number.

The value of x here can only be odd, because odd × odd = odd, odd-odd = even, so that 23-3x can be divisible by 2;

When x= 1, y =10;

When x=3, y = 7；;

When x=5 and y=4,

When x=7, y= 1,

This list is:

To sum up, there are four different arrangements for 23 people to stay in the hotel, with 3 rooms and 2 rooms (there are no empty beds in each room).

Extended data:

General steps to solve one-dimensional linear inequality;

(1) denominator: According to the properties 2 and 3 of inequality, multiply both sides of inequality by the least common multiple of each denominator at the same time to get a small equation with integral coefficient.

(2) Remove brackets: According to the law of brackets, when there is a negative sign outside brackets, special attention should be paid to removing brackets and negative signs and changing the symbols of items in brackets.

(3) Shifting terms: According to the basic properties of inequality 1, generally, the terms containing unknowns are moved to the left of inequality, and the constant terms are moved to the right of inequality.

(4) Merge similar items.

(5) Turn the coefficient of the unknown into 1: According to the basic properties of inequality 2 or 3, pay special attention to that when the coefficient is turned into 1, the coefficient is negative, and don't change the direction without an equal sign.

(6) Sometimes it is necessary to express the solution set of inequality on the number axis.

Baidu encyclopedia-unary linear inequality