<div class='user_solution'><span style="font-size: 12pt; font-family: Arial;">a)</span><br /> <b><u><span style="font-size: 12pt; font-family: Arial;">1.K:c4!</span></u></b><span style="font-size: 12pt; font-family: Arial;"> </span><b><span style="font-size: 12pt; font-family: Arial;">(A)</span></b><span style="font-size: 12pt; font-family: Arial;"><span>  </span>threat<span>  </span>2.B:f6+ Kf8, Kh6<span>  </span>3.Qa8, Qh1#</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kf8<span>  </span>2.Qa6 (B) zz. K:e7<span>  </span>3.Qe6+ (D)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kd8, Kf8<span>  </span>4.Ba5, Qf7#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Ke8<span>  </span>3.Qc8+ K:e7<span>  </span>4.Bb4#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Kg7<span>  </span>3.Q:f6#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>     </span><span> </span>/ 2…Bg7<span>  </span>3.Sg6+ Ke8, Kg8<span>  </span>4.Qc8, Qe6# / / 2…Sf6</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;"> 3.Sg6+ /</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kh6<span>  </span>2.Qf1 (C) zz. K:g5<span>  </span>3.Qf5+ (E)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kh4, Kh6<span>  </span>4.Be1, Qg6#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Kg7<span>  </span>3.Q:f6#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Kh5<span>  </span>3.Qh3+ K:g5<span>  </span>4.Bd2#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>     </span>/ 2…Bg7<span>  </span>3.Sf7+ Kh5, Kh7<span>  </span>4.Qh3, Qf5# / / 2…Sf6</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;"> 3.Sf7+ /</span><br /> <span style="font-size: 12pt; font-family: Arial;"> </span><br /> <span style="font-size: 12pt; font-family: Arial;">b)</span><br /> <b><u><span style="font-size: 12pt; font-family: Arial;">1.Q:a6!</span></u></b><span style="font-size: 12pt; font-family: Arial;"> </span><b><span style="font-size: 12pt; font-family: Arial;">(B)</span></b><span style="font-size: 12pt; font-family: Arial;"> zugzwang</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kf8<span>   </span>2.K:c4 (A) zz. K:e7<span>  </span>3.Qe6+ (D)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kd8, Kf8<span>  </span>4.Ba5, Qf7#</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kh6<span>  </span>2.Qe6 (D) zz. K:g5<span>  </span>3.Qf5+ (E)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kh4, Kh6<span>  </span>4.Be1, Qg6#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span> </span>2…Kg7<span>  </span>3.Qf7+ Kh6<span>  </span>4.Qg6#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span> </span>2…Kh5<span>  </span>3.Qh3+ K:g5<span>  </span>4.Bd2#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>      </span>/</span><span style="font-size: 12pt; font-family: Arial;"> </span><span style="font-size: 12pt; font-family: Arial;">2…Bg7<span>  </span>3.Sf7+ Kh5, Kh7<span>  </span>4.Qh3, Qf5# /</span><br /> <span style="font-size: 12pt; font-family: Arial;">/ 1…Sf6</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;"> 2.Kd4</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;">+ Sf6<span>  </span>3.Q:f6#<span>  </span>2…Kf8<span>  </span>3.Sg6+ /</span><br /> <span style="font-size: 12pt; font-family: Arial;"> </span><br /> <span style="font-size: 12pt; font-family: Arial;">c)</span><br /> <b><u><span style="font-size: 12pt; font-family: Arial;">1.Qf1!</span></u></b><span style="font-size: 12pt; font-family: Arial;"><span>  </span></span><b><span style="font-size: 12pt; font-family: Arial;">(C)</span></b><span style="font-size: 12pt; font-family: Arial;"> zugzwang</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kf8<span>   </span>2.Qf5 (E) zz. K:e7<span>  </span>3.Qe6+ (D)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kd8, Kf8<span>  </span>4.Ba5, Qf7#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Ke8<span>  </span>3.Qc8+ K:e7<span>  </span>4.Bb4#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>       </span>2…Kg7<span>  </span>3.Qg6+ Kf8<span>  </span>4.Qf7#</span><br /> <span style="font-size: 12pt; font-family: Arial;"><span>     </span>/ 2…Bg7<span>  </span>3.Sg6+ Ke8, Kg8<span>  </span>4.Qc8, Qe6# /</span><br /> <span style="font-size: 12pt; font-family: Arial;">/ 1…Sf6</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;"> 2.Kd4</span><span style="font-size: 12pt; font-family: Arial;">~</span><span style="font-size: 12pt; font-family: Arial;">+ Sf6<span>  </span>3.Q:f6#<span>  </span>2…Kh6<span>  </span>3.Sf7+ /</span><br /> <b><span style="font-size: 12pt; font-family: Arial;">1…Kh6<span>  </span>2.K:c4 (A) zz. K:g5<span>  </span>3.Qf5+ (E)</span></b><span style="font-size: 12pt; font-family: Arial;"> Kh4, Kh6<span>  </span>4.Be1, Qg6#<span>  </span></span><br /> <span style="font-size: 12pt; font-family: Arial;"> </span><br /></div>