Problem 1
|
Key: |
1.Qb3 |
|
Threats: |
2.Qe6 2.Qf7 and 2.Qf3 |
|
Variations: |
1...Pe4
2.Qe6
1...Pe6
2.Qxe6
1...B-any
2.Qf7
1...Kf5
2.Qf3
|
The
key gives rise to three threats that are neatly separated. An
additional interesting feature is the thematic try 1.Qg8 threatening
2.Qe6 and 2.Qf7. The two threats are separated after Pawn and Bishop
moves but is defeated by 1...Kf5!.
In this
interesting problem there are as many as six threats after the key
move separated by six defences!
Key:
1.Nd6
Threats:
2.Rc4
2.Re4
2.Rcxd4
2.Rexd4 2.Nb5 and 2.Nf5
Variations:
1...Rxe3
2.Rc4
1...Rxc3
2.Re4
1...Nxe3
2.Rcxd3
1...NXb2
2Nb5
1...Nxf2 2.Nf5
Six
threatened mates are neatly separated in this excellent composition.
In
the first two problems the key moves gave rise to multiple threats.
In this and the next problem, there is only one threat after the key;
the multiple mates (duals) arise after a black defence. Where the
multiple threats arise after the key, the theme is Primary Fleck;
where the duals arise after a black defence, the theme is known as
Secondary Fleck.
Key:
1.Qc7
Threats:
2.Qxd7
Variations:
1...Nb8
2.Qa5/ Qc5/ Qh7/ Qf7/ Qe5
1...Nc5
2.Qxc5/ Qh7/ Qf7/ Qe5
1...Nb6
2.Qh7/ Qf7/ Qe5
1...Nxf8
2.Qf7/ Qe5
1...Ne5
2.Qxe5
1...Nf6
2.Ng7
While
there is only one threat after the key move, there are five possible
mates after the first defence - Nb8. Such a case would normally be
considered a serious defect - dual (more than one possible
mating move - always called dual only even if the possible mates are
more than two); but here the duals are planned and form an essential
part of the theme. Other defences permit fewer possible mates in a
neat progression - 4, 3, 2, 1 and none of the five. As one defence
stops all the five possible mates available after 1...Nb8 a new mate
is provided!
Apart
from the progressive separation of mates the defences in the solution
involve all six possible moves of a knight - an incomplete knight
wheel. The excellent composition packs some very interesting
features in a Meredith setting.
Problem 4
Like
problem 3, here too the theme is secondary Fleck. After the key
move, there is only one threat. A particular defence gives rise to
four possible mates. Other defences provide all possible
combinations of three, two and one of the four mates. We had learnt
in school algebra, under permutations and combinations, the number of
such possible combinations. These are four combinations of three
each, six combinations of two each and four of one each. If the four
mates are A, B, C and D, the 15 combinations are ABCD, ABC, ABD, ACD,
BCD, AB, AC, AD, BC, BD, CD, A, B, C and D. The solution provides
the variations in this order.
Key:
1.Ng4
Threat:
2.Rxe5
Variation:
1...Qe8
2.Qd5/ Ng5/ Rf4/ Re3
1...Qc3
2.Qd5/ Ng5/ Rf4
1...Qh2
2.Qd5/ Ng5/ Re3
1...Qe7
2.Qd5/ Rf4/ Re3
1...Qe6
2.Ng5/ Rf4/ Re3
1...Qg3
2.Qd5/ Ng5
1...Qf4
2.Qd5/ Rxf4
1...Qf6
2.Qd5/ Re3
1...Qd4
2.Ng5/ Rf4
1...Qd6
2.Ng5/ Re3
1...Qh5
2.Rf4/ Re3
1...Qd5+
2.Qxd5
1...Qg5
2.Nxg5
1...Qxc5
2.Rf4
1...Qf5
2.Re3
The
variations showing all possible permutations and combination of the
four mating moves exhibit a skill that would please a mathematician.
An excellent composition showing secondary Fleck theme with 15
defences by the black queen met by a different mate or a different
combination of mates.