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MatPlus.Net Forum General Most squares the Black king could be mated on in one, without being on the board?

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Those are irrelevant in this case, Jacques-refer to Haueke's problems as well. This is the task of White choosing where the Black king goes-in the dual free cases we are exploring all squares must be covered of course

But with mine empty squares are needless to bring up in this little niche-in this case-of giving all available mates to a single piece.

sorry, at least not at all what I intend to do.

If fairy pieces are allowed, the task is easy.

(= 2+1 )

Ubi a1
Mate in 1
SH, original

1.U:b3 mate
60 squaares (all except a1, b3, c2, d3)
Not: 1.c:b3+ K:a1!

(an Ubi essentially is a fairy piece that can moves as if it could make any number of consecutive knight moves, but it can't move on after a capture)

with wK
(= 2+2 )

Ubi a1
Mate in 1
SH, original

1.U:b3 mate
57 squares

anticipated
https://matplus.net/start.php?px=1604858389&app=forum&act=posts&fid=xshowm&tid=595
(16) to (22)

@Jacques: These are simply two different tasks (mate sK on
each legal field/mate on choses fields) and it surely make
With the gained knowledge, one can start then with the former.
@Rewan: Good job. Here is a sketch with promoted material
that might be reduced to beat 8:

(= 10+15 )

btw it seems easy to bring this to 11...

Correct, Jacques :-) I also added a few superfluous figures
such that the bK can only stand on these 11 fields.

(= 11+21 )

nice ! seems a maximum with one rook

Now the King. Cf. my sensational :-) Problem-Forum #521 with some
elaborate dual-avoidance trickery, so the following is
just a first obvious try with 4 batteries, more might
be possible. Again, some "filler" for Jacques :-)

(= 10+9 )

For a bishop, at least 8 can be done. For Jacques, once more as well, all non-BK squares are filled in. :)

(= 12+17 )

Rewan, you are guilty that I don't get any sleep tonight :-)
(And I'm too tired to check it thoroughly. In any case, 10 still might be possible.)

(= 12+18 )

5 for king
(= 13+3 )

Kg8 : Kb5#
Kf7 : Kd3#
Ke6 : Kd4#
Ke2 : Kd5#
Kf1 : Kb3#

I *knew* it :-) (But there are mating duals with the BB. One is easily eliminated
with Ba8->b7,+sBa8, but alas, the board is too small for the other :-( (On a 9*9,
obviously 6 K # are possible with the same idea, so let's go all the way...)

(= 5+19 )

Knew I still could up the ante a bit - and I get no sleep again :-) 13 Q# (no filler)

wonderful Hauke !! and so light!,
A big step !
Anyhow, the fact there is no solution with the king on a4 or d1 is a problem

5 for the king :
(= 11+5 )

1#
b)e1->f3
c)e1->e5
d)e1->f6
e)e1->g7

a)
1.Kc2‡!
b)
1.Kb4‡!
c)
1.Kd3‡!
d)
1.Kd2‡!
e)
1.Kc4‡!

anyhow, here also, the fact there is no mate if the black king is on d1 is a problem (for the other empty squares it is easy to find something to do)

it is all the difference between a succession of twins and a short sentence " wherever the black king is he is mated in one"

In fact, if you refer to the title of this thread "- without being on the board -" you can see easily that if you need to show the places he is, there is something "wrong"

could be utilized.
As I already said, I simply count the distinction "valid even
in Kriegsspiel" and "just a construction" as two different tasks,
the former earning a bit more mojo :-) Feel free to edit my
position even if it might cost one or two mates.

(37) Posted by Hauke Reddmann [Thursday, Nov 19, 2020 10:10]

Update: