<h1>
Solution:
</h1>
<p>
<br>
<b>
Congrats to @theaustrianguy for finding the key move (and thus being the winner of this round)!
</b>
</p>
<p>
The first move is
<br>
<b>1. Ra4!</b> (idea: 2. Rxa7 Rxa7 3. Rd8# checkmate) after which white has a clearly better position in every variation.
</p>
<p>
My opponent responded with <b>1. ... a6</b> (moves like 1. ... Ne7 or 1. ... Kf8 had been somewhat tougher but not sufficient, as well) - see position below:
</p>
<hr>
<p>
https://cdn.steemitimages.com/DQmURFUGZowxmHdbnr7ehvwED2huPAQPRkbVtuyqs49MMGv/Chess_problem66_ZL.jpg
</p>
<hr>
<p>
I guess he didn't expect the answer
<br>
<b>2. Rxa6!</b>.
<br>
He continued with <b>2. ... Rxa6</b> which allowed me to checkmate him immediately:
<br>
<b>3. Rd8#</b> checkmate (the knight at c6 is pinned):
</p>
<hr>
<p>
https://cdn.steemitimages.com/DQmXSvShXKe3xXKi1xA1bnR8x5gEDPiAbgMbbwMHowemV4S/Chess_problem66_L-a.jpg
</p>
<hr>
<p>
However, also <b>2. ... bxa6</b> wouldn't have helped because of
<br>
<b>3. Bxc6+ Kf8</b>
<br>
<b>4. Bxa8</b> and again black cannot prevent the checkmate:
</p>
<hr>
<p>
https://cdn.steemitimages.com/DQmXimMjtdAoZXcvDFjk2BtWiupMzaLsW67Xni5od9Pknja/Chess_problem66_L-b.jpg
</p>
<hr>