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76 CONJUGATE SOUARES<br />
A-r, in thn case representine low asNanss, b1<br />
orb3 = h6orb8. (Two unmarked pairs, c7=e7and<br />
c8=e8, are noi.elevant <strong>to</strong> theplay.) While wanls<br />
10 play K d4 threatening e4 c5,orK-e3threal'<br />
ening K i4, and eithcr would Mn unless Bl.c[<br />
muld rcply immediately... KI6z or... Kg5z<br />
rcspcdively. Thtrs the pans G=g and I(:[ arc<br />
identified. By exlension oulwards all the otner<br />
pairs can be found. For cxanple, if White plays<br />
Kd3 gaining a@ess <strong>to</strong> both d4 d e3, Black needs<br />
<strong>to</strong> reply . . . Kg6z <strong>to</strong> gain acess <strong>to</strong> 16 and c5; ttus<br />
(L3=g6. Bla.k <strong>to</strong> play oulddraw<strong>by</strong> L . . KgTor<br />
I . . Kh7 onrinuing 2 Kb2 Kg8z or Kh6z, or<br />
2 Kb1 Kg6z. Holdins the delensive (nregulao<br />
opposnion. hc can alNays Place whitc in ztrgflang.<br />
White ro play *iN in the same way thal he<br />
wonld win if he held the regnlar opposition: he<br />
holds Bl.ck in zuczwang uniil he can oudank<br />
successfully. _fhc key is 1 Kblz. Two variations<br />
follow: 1 . . Kg7 2 Kciz KS6 3 Kdlz Kg5 4<br />
K.2 (ouina.king) 4...Kn6 5Kd22(h5 6Kc3<br />
(oudanrjng) 6...Kgs 7 Kc4 (oudantins) 7<br />
...Kg6 8Kd3zi 1...KhS 2Kb2z(C8 3(b3z<br />
Kh8 a Kc4 (outflanking) 4...K97 5Kc3zrr<br />
6 Kd2 (outflankina) 6... Kf6 7 Ke2<br />
(oudanking) 7...Kg6 8 Kd3z.<br />
I-ocockt study, the frrst ot its kind, made no<br />
immediate inpact. hsER noted it, and in 1901,<br />
airer winning the world ch<strong>amp</strong>ionship a.d a few<br />
naior loumaments, he constructed a oniugate<br />
sqrare study shich attracted wide inlerest Many<br />
such sludies folloped. In the 192G and 1930s<br />
attempts were nade <strong>to</strong> establkh a conprehemive<br />
classilication oI rhe nany pafterns thal are Po$ible<br />
in conjqatc square positions. Tle results Nere<br />
unconvincing. For exanPle. rhe Li.ock stndy is<br />
supposed <strong>to</strong> sbow the eighr-square synen'<br />
because tbe squarcs .4d4,c3,d3,e3,c2,d2, and e2<br />
arc pairedmi.roFlashion witheighl squarcs on the<br />
other side of the diagonal axh h2 b8. This is a.-<br />
interestina obseNalion, but il accounls lor lewer<br />
than halfthc conjusate pairs. To undestand a se1<br />
of such pairs those that occur when lhe kings are<br />
close roge ther should be di scovc red , a.d Lon this<br />
slarting poinl other pais can be derived.<br />
tr&, xa<br />
7e % 7"&.<br />
tw vg&<br />
%%w<br />
'7& Tlgr<br />
A studv b; MANDTR. wii',, s chochzeitunp. Ts24,<br />
a rare;x;mple oI dnjugate squares ocuPied <strong>by</strong><br />
picces other than kings. <strong>The</strong> kniSht and bishop<br />
6ghl a duel while rhe kin8s and pasns sta.d <strong>by</strong>. For<br />
Black's knight there are 6ve key dark squares, b2<br />
andc5 which gi,c checkmale, e5,95, and i2 when<br />
nate cannot be preve.ted. <strong>The</strong> approach <strong>to</strong> these<br />
is <strong>by</strong> way of 15 light squares, b?, d7, tf , h7, e6, 96,<br />
c,l. e,l,94, b3, d3. fJ, h3, dl, or hl, and the bishop<br />
musl prevent lhe knight lron reaching any on. oi<br />
them. ztrgnangs anse becalse the bishop may be<br />
ablc io defend lrof onlyone squa.e, e.g. with Nl6<br />
wlire needs his bishop on f5, and he annot lole<br />
the nove snouH ii be his turn <strong>to</strong> play.Inherently,<br />
the posirio. cont.i6 36 zugzsangs. <strong>The</strong>e are<br />
irrelevant <strong>to</strong> the solution (Nd8:Bd5. Nl8=8f5,<br />
Na5-Bd5) and 1wo a.e umecessary: whitc may<br />
rcpl! r..<br />
Ng7 <strong>by</strong>Bf5 nol Bdlz. and may repl) <strong>to</strong><br />
Nal hy plaJants hi5 bi\h.p <strong>to</strong> the , 88 didBona)<br />
instead oI Bdtz. For , posnions ot the knighl<br />
White can detend only <strong>by</strong> setting up zugaangs:<br />
Nc8=8I, or Bt:<br />
Ng8=8g6 or Bg4<br />
Ne7=Bh5<br />
Nd6=Bd5<br />
Nf6:Bf5<br />
Nd5=88'1<br />
Nf5=BB<br />
Nd4:Bd5<br />
NI4-B15<br />
Nc3=Be2<br />
Ng3=Bd5<br />
Nc2=BB or B.4<br />
Nd2=Bd5<br />
Ne2=Be6<br />
NC2=Bg4<br />
Ng1=Bg4<br />
Nfl=BB<br />
While <strong>to</strong> play draws <strong>by</strong> I Bh5z alter which he can<br />
always hold Black in zu8dang.<br />
<strong>The</strong> inlomation about conjugate squares .on<br />
rained io standard endgane books is sufficient for<br />
nost pra.tical puposes. Among speoalisl boots<br />
ire Rinaldo Bianchetti. Co"ri bu<strong>to</strong> alla Teoria del<br />
Finole di Soli Pedoni (1,925)t DU.H&. and Il8lr<br />
sr^Dr, L'Oppasition et les cdes coniuge^ sont<br />
ftconcilii* (1932); aad Waltet Bibt. Opposition<br />
u Krnbche Fel.l.t in Boumendspiet (1936).<br />
CONNECTED PAlvN, a pawn thal can guard or be<br />
gudded <strong>by</strong> a pawn o. a. adjoining nle. theternis<br />
tsenerall, used i0 rhepluralL.dehne a groupuflNo<br />
or more sucb pawn(. such a Eroup may include<br />
doubledpawns: for ex<strong>amp</strong>le, after 1 e4 c6 2 d,{