1. Rb5 Ra1 IF BLACK ROOK DEVIATED FROM a FILE 1...Rd2 2.Rxa5+ Kxa5 3.Ra3#

2. Rb2 Ra2 IF 2...Ra3 3. Rxc4# OR IF BLACK ROOK DEVIATED FROM a FILE AGAIN 2...Rd1 3.Ra2#

3. Rxa2#

By the time you have figured all this out at the board, the village idiot would have mated via 1. R:c4+ Ka3 2. Kb5 Rb2+ 3. R:b2 K:b2 4. K:a5 Kb3 5. Kb5 Ka3 6. Rc3+ etc. since none of those moves would take more than a few seconds to play.

that last part got cut off- in short 1.Rb5 Ra1 2.Rb2 Ra3 3.Rxc4#

Black is almost completely immobilized- if the rook moves off the a-file, white just mates starting with 2.Ra1+. So a waiting move is called for- but specifically, I would be looking to allow black to play Ra1 so that I could play Rb2- the idea being that black rook will then be forced to either leave the a-file, or to occupy the a3 square making Rc4 mate rather than just check. A quick look at the possibilities tells me that 1.Rb5 is a mate in three the threat is 2.Rxa5 followed by 2.Ra3# if the black plays the rook off of the a-file on his first move, and if black puts the rook on a1, then 2.Rb2 again threatens mate if the rook leaves the a-file, and also threatens 3.Rxc4#