<div><br /></div><div>a).<br /><br />1. Sf5! c6 2. Bc2 Kb5 (2. ... Ka6? #5) 3. Kd4<br /><br />3. ... Ka5 4. Sd6 Ka6 5. Bd3+ Ka5 6. Sb7#<br /><br />3. ... Ka6 4. Sd6 Ka5 5. b4+ Ka6 6. Bd3# (switchback mate).<br /><br />b).<br /><br />1. Sc2! c6 2. Ba7 c5 3. Kd5 c4 4. Kc6<br /><br />4. ... cxb 5. Bb6+ Ka4 6. Bb5# (ideal mate)<br /><br />4. ... cxd3 5. Bb6+ Ka6 6. Sb4# (model mate)<br /><br /> (4. ... c3? 5. Bb6#)<br /><br />Including short mates, all white pieces mate and all are used in both solutions. Passive bishop sacrifice in b.[A]</div><br />