### Solutions pour Mort Subite
Navré, il me manque le temps a ce moment pour soumettre les solutions
en français. Pourquoi pas envoyez-moi
les *vôtres*? Points de grammaire ou d'autographie sont également
bienvenues!
**{A}** If the ep is off, then the position is dead. **0...Kb7*Ma6**
(where M is a mystery, possibly 0) would have been forced. So by
elimination, the last move was **0...b7-b5** and the ep is *on*.
The game is alive. [I was just a few weeks ahead of the very able François
in developing my own versions of the themes shown in {A}, {B} & {C}.
Phew! The most economical version of the theme in {A} is François' own
{J} here.]
**{B}** Again, if the ep is off, then the position is dead. **0...d6xc5**
would have been forced. So by elimination, the last move was as expected **0...c7-c5**
and the ep is on. **1 dxc5ep bxc6+ 2 Ka6 ad lib 3 b7#.**
**{C} **If castling rights have been lost, the position is dead,
since Black has at most one more move. **0...Ka7*Ma8** would have been
forced. Note the cute try **1 Ke2?** but **1...cxd3+**. So by
elimination, castling must be OK. **1 0-0 cxd3 2 Ra1#. **[This one is
much more economical than my own corresponding {C} here.]
**{D} **The position is dead. **0...bxc2** would have been
forced, so the last move was **0...fxMg2**. M=Q implies an impossible
check, M=P imprisons the Black king, M=R mean Black's move was forced. So
M is minor. The alternative **0...f3-g2+** is answered only by **1
Nxf2=**. But **0...f3xe2** if M=B allows **1 Bg2-f1 e2xf1=Q**, for
a quick end with the weaker side winning, but promoting to anything else
still keeps the game alive. [I must confess: I tweaked this one again as I
wrote the solution here.]
**{E}** The position with check is followed by **1 Qd5+ Bxd5+ 2
Rxd5=**. Black's last move was **0...Bh7xMg8**, but only M=B allows
the check chain to be broken by **0...Be8-f7+ 1 Bg8xf7 Bh7-g8**, etc.
(M=Q is not possible because the wQ and all 8 wPs are already on the
board.)
**{F}** Once again, if the ep is off, then the position is dead.
Could the last move have been **0...Kb8xNa7**, after **-1 Nc8*a7+**?
No because it would have been forced. So the ep is legal and mates.
**{G}** The position is dead. The only preceding move with choice is
**0...e3-d2**.
**{H} **The joke here is that both sides undergo stalemate in
different lines. As before, if the ep is off, then the position is dead. **0...b6-b5**
has alternative **0...bxa5=**. So by elimination, the pawn double step
is the badger, and **1 axb5ep** keeps the game alive. [This position is
crying out to be dedicated to someone: Kasparov?]
**{I}** (by Nicolas Dupont) Mate in 1 can only be achieved via
cxd6ep# or gxf5ep#. Hence we have to show that the last Black move must
have been d7-d5 or f7-f5. Let's consider all other possibilities:
Why not a king move? Because 1) squares d6, d8, f6 & f8 are doubly
controlled 2) squares d7 & f7, are only singly controlled, but the
last White move can't have been Pe6+, since there are pieces on d5, e5
& f5. [This last is not true, surely, since d7 & f7 are doubly
covered. Maybe Nicolas means to have a knight on e8 not a bishop?]
Why not d6-d5 or f6-f5? Because of the White king in e5.
Most interestingly, why not c6xMd5 or g6xMf5 (where "M" is some
unknown unit)? Because the position is already DEAD before such a move!
So cxd6ep# or gxf5ep# is available.
Notice that the solution to that problem is really unique, although it's
impossible to determine which capture would be valid! This is an example
of the Partial Retro Analysis (PRA) convention at work.
**{J} **The position is dead, and **0...Bg3*Mh2** has a live
alternative in **0...Bg3xf2** only if M=0 so **1 Kh2** keeps the
game alive.
**{K}** The trick is that if White just moves the king towards a7,
Black will promote to a bishop, and the game is dead. 1 Bb4 then if 1...f3
2 Kd4! (2 Kc4? f2!). On the other hand if 1...Ke7 2 Kc4! (2 Kd4? Kd6!) [I
wonder if this one could be tidied up? At least make it a corner square wK
is aiming for.]
**{L}** Another regicide capture-fest, remorselessly sliding into
pat. **1 N~-c8+ Qxc8 2 N~xc8+ Rxc8 3 Kxc8 Rh8+ 4 Qd8+ Rxd8 5 Kxd8+**.
How could Black have avoided this? **0...Q?xMd8** was the last move.
Retro logic states that the only candidate for M is B. So Black was in
check already. If bQ was on e/f8, then there is no choice. But bQ on e7
allows: **0...Rg8xd8+ 1 N~c8+ Rd8xc8+ 2 N~xc8# **perhaps. So **0...Qe7xBd8+**
was last move.
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