Seeing vs calculating

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White to move.
You can find the solution here.

I always say that we should seek speed in doing something different and not by trying to do what we already do at a higher speed. You can move faster by changing from walking to using a bike. You can never speed up walking to the same extend as riding a bike.

Especially in a position like the above, I feel that it should be possible to actually see the solution right away in stead of calculating it.
Allthough the problem has a rating of 2282, and people found 19 moves that go astray, the problem is rather clean and straightforward.

The tactical elements are easy to spot:

• Discovered attack Qd1, Nd4
• Discovered attack Re1, Ne4
• Pin Bg5 => Nf6
• Knight fork Nxf6 => Kg8, Re8

One of the discoveries while doing high rated tactics is that I always neglect the defenders. But the defenders often give a clue where to start the combination.

In order to see the combination, it is necessary to see the essence of the position. This essence consists of seeing the tactical elements and seeing which pieces defend which. In stead of seeing the bare pieces, you can see the function of the pieces. What they are actually doing.

• Qd8 is defended by Re8.
• Re8 is defended by Qd8, Ne5 and Nf6
• Ne5 is defended by Re8
• Nf6 is defended by Qd8 and Bg7

This gives an idea of the load of the defenders:

• Qd8 defends 2 pieces.
• Re8 defends 1 piece.
• Bg7 defends 1 piece.
• Ne5 defends 1 piece.
• Nf6 defends 1 piece.

So the queen is overloaded.

All this you can see in one mental picture. That means:

• Seeing the pieces.
• Seeing the attacking elements.
• Seeing the defenders.

It is possible to see this all at the same time. To mentalize it is maybe a better word.

Of course you might not be able to see it right away, may be you should do first some trial and error in order to reveal the tactical elements and the defensive elements. But once you have listed these elements, you can mentalize them. It may take you a while before you are accustomed to the picture. Once you become familiar with it, you will be able to look around in the picture and see more details. It is for instance possible to look at Bc8 and Ra8 and see that they don't play a role in the combination.

You can compare it a bit with looking at a stereogram. At first you will have trouble to focus. But after some exercises you will be able not only to focus, but to look around in the picture while maintaining focus. Just like you would look around a normal 3D object.

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The queen is overloaded, so that gives a clue where to start the combination. The idea behind overloading is to attack one of the pieces that is defended by the queen so that she has to commit herself and leave the other piece that she defended without defence. Knight f6 is already under attack.
First you must get rid of the second defender of Nf6 which is Bg7. An exchange will do that. But with what piece should you start? My instinct is inclined to start with the knight, in order to keep the pin. But Nf6 is subject to two attacks: a knight fork and a pin. It is good to keep the strongest threat, which is the fork (since the King is the target). So you start with 1.Bxf6 Bxf6

Then you must look at the other piece that the queen defends : Re8
Re8 has a second defender too, so you must get rid of that too by a knight sacrifice:
2.Nc6

Here black has two responses: 2. ... Qxd1 or 2. ... Nxc6
After Qxd1 you see why is was important to keep the stronger threat Nxf6. Since you attack the king which prevails over the tackeback of the queen.
After 2. ... Nxc6 3.Nxf6+ the queen is forced to abandon Re8, so white wins the exchange.

You see that again a high rated problem is made simple. This is the technique:

• List the attacking elements.
• List the defensive elements.
• Mentalize the position with pieces, attacks and defenses until you can look around in it without loosing focus.
• Apply some straightforward logic, starting by the (lack of) defenders.

This is what I'm dabbling around with lately.