Black is down a Rook. How can Black save the game? 
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1…Bxe5+, 2.Qxe5 Rc8# or 2.Rc7 Bxc7#
2.Qxe5+ is a check (and black gets mated)
Rf1+
Qxf1 Bxd4+
(if white plays Qf2 then black plays Qg3+ and white plays Kf1 and black takes Bxf2 and white recaptures with the rook Rxf2 and white plays Qd3+ and black has a perputual as the white king must always stay near the f2 rook to protect it)
Rf2 Qg3+
if Kh1 Qh4+
Kg2 Qg4+
Kh2 Qh4+
Qh3 Qxf2+
Qg2 Qh4+ with perpetual
if Qg2 Bxf2+
Kf1 Qd3+
Kxf2 Qd2+ with perpetual
1. – Rc8-c1+ 2. Qd4xc1 Qh3-g3+ and now:
3.Qf1-g2 Qg3-e1+ 4.Qg2-f1 Qe1-g3+
or
3.Kg1-h1 Qg3-h4+ 4.Kh1-g2 Qh4-g3+ 5.Kg2-h1
or
3.Rc2-g2? Be5xd4+ 4.Qf1-f2 (4.Kg1-h1 Qg3-h3+ and mate in two) Bd4xf2+ 5.Kg1-f1 Qg3-h4 6.Rg2xf2 Qh4-h1+ 7.Kf1-e2 Qh1xe4+ etc
i’m too lazy …
1. … rf1+
2. qxf1 bxd4+
3. rf2 qg4+
and checks on d1 and g4 and h3 will make perpetual, won’t they?
sincerly, Vohaul
Bxd4+ Qxd4 Rf1++ or Bxd4+ Rf2 Bxf2++
TFK
1…a5
ha ha ha
1….. Rf1+
2 Qxf1 Qg3+
3 Kh1 Qh4
4 Kg2 Qg3
draw by rep.