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Problems with many kings
by Kjell Widlert. International master in composition 1992

As Denmark and Sweden are among the few surviving monarchies, I think it fitting to discuss the problems with many kings here (should I have written about Republican Chess instead?).

Diagram 1
Bror Larsson
Aftonbladet 1930
#3 4+2

Why not 1. Rd3 ~ 2. Ra3# in diagram 1?
Because of 1. - h1K! As white has obviously promoted a pawn to a king, black must have the same right.

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This sort of joke problems gained respectability when the serious fairy form Rex Multiplex was introduced some 30 years ago. The idea is that all kings from the same side must be mated simultaneously.

Diagram 2
Fritz Hoffmann
Feenschach 1983
S#3 Max.
Rex Multiplex

Diagram 2 illustrates this, but also a special situation that must be considered. After 1. g8R Bh1 2. Rg2 Qxg2 3. d8B, the longest move is 3. - Qa8 ... which brings problems: the white kings are not mated, but white can't go on playing because whatever he does, at least one king will be left en prise. What to do? Answer: 3. - Qa8? is illegal! In Rex Multiplex, we must have the rule that a checking move is legal only if all kings are mated or all checks can be parried by one move. So black's longest legal move here is 3. - Qb7#, mating both kings as planned.

Diagram 3
Kjell Widlert
V., 1 HO Feenschach 23 TT 1971
#3 Rex Multiplex 8+4

The special rule can be used in other ways. In Diagram 3, black would be in zugzwang after 1. Sf3 Sc4 but for the unpleasant check 2. - Sb6+. This can be stopped by 2. a8K! (2. - Sb6+ is now illegal) and it follows 2. - S~ 3. Qd2#. Similarly 1. - Se4 2. g8K! S~ 3. Qd2#. By-play 1. - Sxf3 2. Rb2.

Diagram 4
Kjell Widlert
V. 1 PR Feenschach TT 1971
#3 Rex Multiplex 8+7

Instead of arranging a check on two kings as in diagram 3, white can arrange a mate on just one king with the same result. In Diagram 4, 1. - Qa2? is illegal: Black hasn't mated both kings (only one of them), but white cannot go on playing, so the move is illegal. Solution 1. Sc5 (thr. 2. Sb3#) Sd4 2. Ra4! and now 2. - Sxb5? is an illegal check(mate) as white doesn't have 3. Ka4?? So there follows 2. - S~ 3. Sb3# (or 2. - B~ 3. Bxb2#). Analogously 1. - Sd2 2. Ba4! S~ (Sc4??) 3. Sb3#.

The idea of Rex Multiplex to have "ortodox" mates with many kings introduces some more difficulties. What if there were a wSa5 in diagram 2, pinned by a bRa1 – would 4. Sxb7?! be possible? It doesn't make a difference to wKa6, but it saves the wKc8. So would the white kings really both be mated? We need another special rule for this case.
The fairy form in diagram 5 avoids all such difficulties in a beautifully simple way. The rule here is, that one side is mated, if he cannot save all his kings from capture - so at least one king will stay en prise. If this rule had applied to diagram 3, 3. - Qa8# would have been mate rather than illegal. Salazar is the inventor and named the form "Siamese kings", I have added "Salazar" to avoid confusion with another form of Siamese pieces.

Diagram 5
Francisco Salazar
Problemas 1969
#2 Salazar Siamese kings 9+8

In Diagram 5, the key is 1. Sxd3! threatening 2. Sg5#: Ke4 is en prise, and if black tries 2. - K4xd3 the other king on e2 is en prise instead. So black cannot save both kings: he is mated. This method of threatening one king in such a way that he can only escape by exposing the other king is one of the three ways to mate in this fairy form. The other two also occur in this problem: 1. - K4f3+ 2. Sd4# with a fork on both kings, and 1. - K2f3+ 2. Qf2# with a normal mate to one king. There are two more thematic crosschecks: 1. - K4xd3+ 2. Sf4#, 1. - K2xd3+ 2. Qc2#. Byplay 1. - Sfe7 2. Qe3#, 1. - Sge7 2. Qe5#. I believe Salazar always used 2+2 kings, but the principle can be applied to any number of kings.

There is another way to deal with many kings. We can say that one side is in check only if all his kings are en prise. As always, he is mated if he cannot stop the check.
I invented this rule many years ago, calling it Ultra Rex Multiplex, but this is the first publication. Let's have a look at Diagram 6.

Diagram 6
Kjell Widlert
#2 Ultra Rex Multiplex 11+11

Black is not in check as only one king is en prise. White must attack the other king, but 1. Sd6+ or 1. Se7+ is met by 1. - Ra3! and now Ka7 is no longer en prise. The key 1. Qf1 threatens 2. Qxf4#, but exposes the white kings to checks from Se5. Moves such as 1. - Sxc6+ don't stop the threat (2. Qxf4# saves Kc7 and puts Kf5 en prise), so the S has to go to d3 or f3. 1. - Sd3+ 2. Sd6# saves Kc7 and mates as black no longer has 2. - Ra3 (not 2. Se7+? Qxe7+! dual-avoidance by unpinning).
Similarly 1. - Sf3+ 2. Se7# (not 2. Sd6+? Bxd6+! dual-avoidance by unpinning). Byplay 1. - Ka6 or Kb6 (2. Qxf4? Kb5!) 2. Sd6# or Se7# (alas, a dual), 1. - Rd3 or Rf3 2. Sh4#.
One question remains: is it legal to actually capture a king (a move such as 1. Rxa7?!). I think it should not be legal, but both interpretations are possible.