We begin with a famous problem from Sam Loyd. Notice that the bQ's guard on b4 and e7 prevents the wS from mating - this is the focal position. Moreover, there are mates set for just about every black move, except 1...Qe1,Qe4 in which case the bQ maintains her focal control over b4 and e7. The wPg2 is a famous nightwatchman - it is superfluous but it offers the tries of 1.g3? 1...Qe4! 1.g4 1...Qe1! Instead the flight giving key 1.Be5 blocks the e-file to break the focal control. You can see Loyd's careless construction here. The wBd1 is an extremely wasteful way to place the wK and the wRs are a little bit over overkill. I prefer David Shire's version below with two less pieces and considerably less force. The wBg3 makes all the tries and the use of the wK is outstanding.
From Loyd to Mansfield we see a change of focus with a complete change mutate. The wSf1 controls the bR in the set position:
1...R on file 2.S1d2
1...R on rank 2.Sg3
There is no way to hold the block so the wQ takes over the control of the foci.
1...R on file 2.Qe2
1...R on rank 2.Qg6
Focal play can often lead to duals. For example, in the above Mansfield problem the 1...Re2 unguards both the foci e2 and g6 so is met by 2.Qxe2/Qg6. The problem to the right does not have this flaw, i.e., it has dual free focal play. The initial position is a complete block and a waiting move will hold the play. 1.Rc7? 1.Rc8? offer nice tries but interfere with the wQ's lines and are countered by 1...g4 and 1...Rg3 respectively. The only move that holds the position is the surprising 1.Qh2! Excellent construction.
Now for something a little more complex. The key 1.Qf6! threatens 2.Sf5 and puts the wQ right in the crosshairs of the rooks, which are each doing double duty now. What follows is wonderful battery play based on the foci of the bRs:
Now we turn to a try play problem. There are mates set for the wQ 1...f2/dxe5/Bg2~ 2.Qxg2/Qxe5/Qa2. Moreover the wSs can overload the bB on g5. But which one should it be and to which square. 1.Sg4? handles 1...Bd8/Bh6 with 2.Se3/Sf6 but falls to 1...Bxc1! 1.Sh5? handles 1...Bd8/Bh6 with 2.Sf4/Sf6 but falls to 1...Be7! This is a theme A defense: Black closes the line of guard to e5 to defeat the White mate which will close a second line of guard to e5. 1.Sf5 prepares 1...Bd8/Bh6 with 2.Se3/Se7 but goes down to another theme A defense 1...Bf4! Finally 1.Sg6 does the trick. Interesting enough the wSg7 is camouflage and only there for the tries! It does make for a nice 4x2 Zagoruiko.
Here is another try play problem. There is a battery pointed at the bK on the a-file and a half-battery along the first rank and the bRs are doing double duty on each of these lines. It looks like wBg1 should break the focal control of one of the rooks: 1.Be3? (2.Sh2) 1...Rd6!
1.Bh2? (2.Se3) 1...Rd8!
1.Bb6 (2.Sc8) 1...Re4!
Thus it appears that the bRs can handle the two batteries. So White must form a third battery!
Thus the white mates that are forced were the original threats that were defeated by the same black moves in the try play: the Dombrovskis paradox tripled!
Finally here is my work on focal play. It was my first problem to appear in the The Problemist. The bQ holds guard on d5 and f5. It seems that wS h2 will break the guard:
Thus it turns out that wSf6 must break the focus, but this changes the threat!
I probably should have put a bP on c2 to avoid a dual after 1...Qa2.