The logic of counting

 I have a set of 100 tactical problems. I use this to get a better idea of what salient cues I need to solve the problems. While investigating them I noticed different categories in which to divide the logic that is exposed by the problems. One such category is counting.

Diagram 1. Black to move

5rk1/2p4p/1p1p1qpb/p1nPp3/2P1P3/1PN1B1Pb/P3B2P/2Q1R1K1 b - - 0 26

Pinho, P. vs. Gallagher, J., Gibraltar 2013

Attacking is about invasion. In order to decide where to invade, I need an overview of the focal points on the board.

Diagram 2. Same position. Black to move

 Red digits indicate the squares where white has the upper hand. Green digits indicate where black has the upperhand. The logic that I want to develop revolves around the invasion squares. Luring and trading and clearing and chasing etc. are the tools in the box to change the balance on the invasion squares. The salient cues are: a Queen on g2 or f1 is mate.

Although black has the upperhand on f3, he cannot make use of it due to the value of his attacker (the queen). So the first logical question is: is het possible to lure the defender of f3 (Be3) away?

• 1. ... Nd3 forking Q and R with tempo
• 2. Bxd3 Qf3 threatening mate in 1

Diagram 3. After 2. ... Qf3. White to move

White must prevent the mate on g2 now. 

These are the options:

• 3.Qd2
• 3.Re2
• 3.Bf1

Let's have a closer look at the position after 3.Qd2

Diagram 4. After 3.Qd2. Black to move

We must first see how the balance on the focal points has changed.

Diagram 5. Same position. Black to move

As you see, the balance on the focal point has shifted dramatically. This means that it is now time to look for overloaded pieces.

• Qd2 must protect both g2 and e3
• Re1 must protect bot f1 and e3

From here it is easy to see that 3. ... Bxe3+ must lead to the abandoning of one of the focal points where black can deliver mate (f1 and g2).

By focusing on the focal squares and their defenders, a logical narrative unfolds itself.