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(a) 1.Rd3 ( threatening checkmate with 2.Ra3# ) Qh1+ 2.Ka2 Rxb2+ ( 2. …Rb3 3.cxb3# or 2. …Qc1 3.Ra3# ) 3.Kxb2 Qa1+ ( 3. …Qb2+ 4.Kxb2 e5 5.Ra3#, 3. …Qf3 4.Rxf3 e5 5.Ra3#, or 3. …Qh3 4.Rxh3 e5 5.Ra3# ) 4.Kxa1 e5 5.Ra3#
(b) 1.Rd3 Qg1+ 2.Qxg1
(b1) 2. …Kxa5 3.Qc5+ Rb5 ( or 3. …Ka4 4.Ra3# ) 4.Ra3#
(b2) 2. …Kb5 3.Qb6+ Ka4 ( or 3. …Kc4 4.Rd4# ) 4.Ra3#
(c) 1.Rd3 Qxc2+ 2.Kxc2 Rxb2+ 3.Kxb2 e5 4.Ra3#
(d) 1.Rd3 Qg3 2.Rxg3 Rxb2+ ( or 2. …Rb3 3.cxb3# ) 3.Kxb2 e5 4.Ra3#
(e) 1.Rd3 Qh3 2.Rxh3 Rxb2+ ( or 2. …Rb3 3.cxb3# ) 3.Kxb2 e5 4.Ra3#
(f) 1.Rd3 Rxb2+ 2.Kxb2 Qxc2+ ( 2. …Qg3 3.Rxg3 e5 4.Ra3# or 2. …Qh3 3.Rxh3 e5 4.Ra3# ) 3.Kxc2 e5 4.Ra3#
(g) 1.Rd3 Rb3 2.cxb3#
P.S. There are other (a) variations. They are as follows :
1.Rd3 Qh1+ 2.Ka2 Qd5+ 3.b3+
(Ⅰ) 3. …Rxb3 4.cxb3+ Qxb3+ 5.Rxb3 e5 6.Ra3#, Rb4# , Qa3#, or Qb4#
(Ⅱ) 3. …Qxb3+ 4.cxb3+ Rxb3 5.Rxb3 e5 6.Ra3#, Rb4#, Qa3#, or Qb4#.
1…Qg1+ 2. Ka2 Qxd4 3. b3+ Rxb3 4. cxb3#
1….Rxd4 2. b3#
1…Qb8 2. Ka2 Qb5 [2…Rxd4 3. b3+ Qxb3 4. cxb3#] 3. Rxb4+ Qxb4 4. b3+ Qxb3 5. cxb3#
1. Rd3 Qh1+ 2. Ka2 Qd5+ 3. RxQ exd5 4. b3+ Rxb3 5. cxR#
Nullify move Kb2. I meant Ka2.
Very good! Also, 1.Rd4, 1.Ka2 and 1.b3 win.