Suppose there are infinite coaches with infinite members in each coach. They stay at the hotel for infinite days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room every day such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms every day). How can we achieve that?

I tried solving the problem using the following method:

1. I allotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?

Suppose there are infinitely many coaches with infinitely many members in each coach. They stay at the hotel for infinitely many days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room every day such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms every day). How can we achieve that?

I tried solving the problem using the following method:

1. I allotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?

Suppose there are infinite coaches with infinite members in each coach. They stay at the hotel for infinite days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room everyday such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms everyday). How can we achieve that?

I tried solving the problem using the following method:

1. I alotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?

Suppose there are infinite coaches with infinite members in each coach. They stay at the hotel for infinite days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room every day such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms every day). How can we achieve that?

I tried solving the problem using the following method:

1. I allotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?

Suppose there are infinite coaches with infinite members in each coach. They stay at the hotel for infinite days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room everyday such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms everyday). How can we achieve that?

I tried solving the problem using the following method:

1. I alotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?

Suppose there are infinite coaches with infinite members in each coach. They stay at the hotel for infinite days. I know that guests can be accommodated using various methods like the prime powers method, but there's a slight variation in the question which is that the guests have to change their room everyday such that one guest can't occupy the same room again (i.e., they have to occupy unique rooms everyday). How can we achieve that?

I tried solving the problem using the following method:

1. I alotted rooms using the prime powers method.

2. The next day, guests move from their current room $x$ to the new room $x+c$.

I'm struggling after this step. Can someone please help me out?