<div class='user_solution'><span class="MsoNormal" style="text-align:justify;display:block;"><b>Themes: a) Ending that culminating in matte and b) ending of rook and knight against knight and pawns </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>1.Nb6+! </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>Try :</b> 1.Re4? Nb4+ 2.Rxb4 Nxd3 3.Rb1 Nb4+ 4.Kc5 Nd3+ 5.Kc6 Nb4+= positional draw</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>1...cxb6 2.Rc4! </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>Try :</b> 2.Re4? Nb4+ 3.Kxb6 Nd5+ 4.Nxd5 d1Q 5.Re8+ Kd7 6.Nf6+ Kd6 7.Ne4+ Kd7= positional draw</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>2...axb5 </b></span> <span class="MsoNormal" style="text-align:justify;display:block;">2...Nc3 e.g. 3.Be2 Nxe2 <i>(3...h2 4.Rh4+-) </i>4.Kxb6+ Kd8 5.Re4 d1Q 6.Re8#</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>3.Re4 Nb4+ 4.Kxb6 Nd5+ 5.Nxd5 d1Q </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>main</b> 5...Nxd3 6.Rd4 d1Q 7.Ne7+ Kb8 8.Rd8#</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>6.Re8+! </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>Try (a) :</b> 6.Ne7+? Kd8! <i>(</i>Not <i>6...Kd7 </i>? <i>7.Bxb5+ Kd6 8.Nc8+ Kd5 9.Bc6#) </i>7.Nc6+ Kd7 8.Rd4+ Ke6 9.Bc4+ bxc4 10.Rxd1 Ng2 /d3=</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>6...Kd7 7.Nf6+ Kd6 8.Ne4+ Kd5 </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>main </b>8...Kd7 9.Bxb5#</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>9.Nc3+ Kd4 10.Nxd1 Nxd3 11.Rd8+ </b>! </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>Try (b) :</b> 11.Rh8? Nf4! 12.Nf2 g5 <i>(12...b4? 13.Nxh3 Nd3 14.Ng1 b3 15.Kb5+-) </i>13.Kxb5 Ke3!=</span> <span class="MsoNormal" style="text-align:justify;display:block;"><span> </span>or 11.Kxb5? g5 12.Rg8 Nf4 13.Rxg5 h2 14.Nf2 Nh3 15.Rg4+ Ke3 16.Nh1 Nf2 17.Rg3+ Kf4 18.Rg2 Nxh1 19.Rxh2 Ng3=</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>11...Ke4 </b></span> <span class="MsoNormal" style="text-align:justify;display:block;">11...Kc4 12.Ne3+ Kc3 13.Kxb5+-</span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span> <span class="MsoNormal" style="text-align:justify;display:block;"><b>12.Rh8 Nf4 13.Nf2+ Kf3 14.Nxh3 Nxh3 15.Rxh3+- </b></span> <span class="MsoNormal" style="text-align:justify;display:block;"> </span></div>