(1) Lucena
1497

Diagram It's white to move and win, but I doubt that anyone would discover it over-the-board without some knowledge of Lucena.

1.Rg2+
First, move the black king away and give the white king a chance to move out.

1...Kh7
Approaching the rook as quickly as possible

2.Rg4
Here's the key move. White sees ahead to move 7, the first steps of "building a bridge"

2...Kh6
Trying to reach the rook

3.Kf7
The threat, of course, is e8(Q)

3...Rf1+
Getting behind the pawn and capturing it is not an option. White can mate with a king+rook vs king. Can black check the king perpetually?

4.Ke6 Re1+
Continuing the attack on the king or the pawn will queen

5.Kf6
Not Kf5? or Kd5? when black draws with Rxe7. The additional threat is Rh4#

5...Rf1+ 6.Ke5!
Everything is coming together. Again, the threat is e8(Q)

6...Re1+ 7.Re4
And white queen's. Not bad for 1497! 1-0