Assault with Battery--5/5 solved

[Coyote]

While a chess player might speak of moving a piece to give discovered check, a problemist would say he had fired a battery, and call the piece that uncovered check the firing piece. (Actually, it's a little more complicated than that, but indirect and masked batteries will have to wait for another time.)

When there's two firing pieces on the battery it's called a half battery, and that's the subject of this collection. In a typical half battery two-mover the puzzle is, of course, determining which of the two firing pieces should be moved off first. Often there's the additional challenge of choosing the right destination square for either piece, from several plausible options. Here's a simple illustration:

B. Barnes, 1961

[Zag]

I assume these are all supposed to be "White to move. Mate in 2"?

I'll take a stab at #1.

1. You have to pin both the knight and the bishop, or else they can delay the checkmate. Also, you have to pin the knight first, or it can take the pawn on h6, which leaves the king an escape by taking the knight on g7. However, I haven't been able to come up with any reason for choosing one rook in one direction and the other in the other direction, though I'm sure there must be one. Anyway:

1. Rf5 (pinning the knight). black makes any move
2. Rb8#

Oh, now I see it, and I got it right by luck. If you use the rooks the other way. i.e.
1. Rf4
then 1. .. Ba6 stops you from moving 2. Rc8

[Coyote]

I knew I'd end up forgetting something! Yes, they're all mate in two moves, a fact I'd meant to mention before I got engrossed in typing up all those diagrams, honest.

As for your reasoning, it's right on target, except for one false assumption.

By the way, how do you respond to 1...Bb5?

[Zag]

I think I have #2, also. This is so exciting! I hardly ever get your Chess problems, Coyote. Since there is a high probability I've screwed up, I don't feel bad about grabbing two of them.

#2.
1. Nd2 (blocking Rxa2)
if 1. .. Rxd2 then 2. Rxf4#
if 1. .. Bf5 or Bd3 or Rc4 then 2. Qg7# (now that rook is protected by B on a2
if 1. .. Bg8 or Rg4 or any other moves then 2. Re4# (blocking Rc4)

[Zag]

[lostdummy]

Ah, was just about to post my solution for #2, when I noticed Zag already did ;p

But not sure it would work, since :
if 1... Rxd2 then 2. Rxf4+ would allow 2... Bf5 3. Rxf5# makes it mate in 3, not 2
or
if 1... Rc4 we can not do 2. Qg7# , since 2... Kxe6, that Rook is not protected by B anymore

But what maybe could work is:

1. Nd4

if 1... Rxa2 or 1... Rc4 or 1... Rxd4 then 2. Qg7# (since rook at E6 is protected by both Knight ant Bishop)
if 1... Rg4 or 1...Rg2 (to prevent Qg7#) then 2. Re2# (this is why 1. Nc5 wouldnt work, need to prevent both black Rooks from stopping white Bishop from mate)

[MNOWAX]

for #1 i have 1:Rc8 ... then 2:Rf4++


For #5 i have 1:Re2 for the pin of the pawn, then ... 2: Rxf3++ this stops the movement of the pawn to make a hole for the king

For #3 I have 1:gRXa2 ... so that 2: fRa3++ will pin the Knight

thats what i have got for now.
_________________
The Man The Myth The Legend
MNOWAX

[Trojan Horse]

Man. #3 was tough. Everything I tried seemed to have a single loophole.

I think I finally got it, but knowing me, I probably missed something. Here's my proposal.

1. Rf6. Possible replies:

1. ... Rxg1 2. Rxg1#
1. ... Rz1 2. Rz2# (where z is any other file you want)

1. ... h2 2. R on g2 moves wherever, mate

1. ... B moves 2. Rg7#

1. ... N moves 2. Rxa2#

1. ... RhZ 2. RgZ# (where Z is any rank you want)
1. ... Rg7 2. Rxg7#
1. ... Rf7 2. R on g2 moves wherever, mate

So? Did I get it?

[Trojan Horse]

MNOWAX: for your #3, I reply 1. ... Bf6. I'm then all set to play 2. ... Rb7 against your supposed second move.

[Coyote]

We have a winner! Trojan Horse has solved #3...but before I make any comments on that or any of the other posts let me say:

I'm not going to use invisible text on any of this, so if you're the sort of hardcore solver who doesn't want any hints at all you need to stop reading right NOW!!

Ahem. So, as I was saying, Trojan Horse nailed it--the rook has to move to f6 to cut off black's bishop from moving to g5 and cutting off the other white rook from moving to g7 and cutting off the black rook so it can't move to b7 and cut off the white bishop. A chain of dominoes on a chessboard--go figure. As TH pointed out, 1.Rxa2 is defeated by 1...Bf6. A few other near misses (i.e. first moves that are defeated by a single black reply) are:

1.Rg7 Rxg1
1.Ra3 Bg5
1.Rf7 Rxf7

A few comments on the other problems:
for problem #1 This is turning out to be more difficult than I'd expected! So far we have:
1.Rf5 Bb5
1.Rf4 Bb6 (pinning the rook!)
1.Rc8 Bc4
There's not much left to try now, but I feel obliged to point out Zag's erroneous assumption: it's not necessary to pin the knight first. Once the bishop is pinned, when the knight captures h6 it can no longer interfere with white's bishop and white can simply move the other rook to guard g7.

for problem #2 1.Nxd2 I'm not sure what lostdummy was driving at with the 1...Rxd2 2.Rxf4 comment...I'm assuming it's a typo. Pretend I didn't say that last part, and replace it with 'I'm an idiot who was looking at the wrong rook!' 1...Rxd2 still won't prevent 2.Qf7# though. But 1...Rc4 is indeed a sufficient response. However, there's also a problem with 1.Nd4, namely 1...Be7.

for problem #5: This is probably the trickiest one of the bunch--there are upwards of ten plausible choices for the two rooks for their first move. However, I don't think confusion over pawn directions should be part of the puzzle! I suspect MNOWAX is assuming the black pawns are moving up the board, so let me remind everyone that black is starting at the top of the board in all these problems. In any case, 1.Re2 is answered by 1...Qd6 regardless of pawn direction.

[MatthewV]

For #1
I was thinking of [Re5

If the knight kills the rook, Rfx
If the black bishop goes e7, Rb8
if the white bishop goes b5, Re8
]

[lostdummy]

For #2:

yes, it seems I didn't notice 1...Be7 ;p

but in meantime I noticed that I don't need to prevent both black rooks (due to pin on black king from Rf1) , so actually:

1. Nc5 can work, threatening 2. Qg7#

if 1... Rxa2 or 1... Rc4 then 2. Qg7#
if 1... Rg4 (to prevent Qg7#) then 2. Re4# (since Rf2 cannot move due to pin)
if 1... Rg2 (to prevent Qg7#) then 2. Re2# (since Rf4 now cannot move)

For #5:

it seems like 1. Rd4 can work, threatening 2. Rf6#

if black try to threaten white queen, then Rf5 moves to prevent threat and still its mate:

1. ...Be8 2.Rf7# or
1....Ra6 2. Rf6# or
1... Qd6 2.Rf6# or
1... gxh3 2. Rg5#

if black try to position figure to put on diagonal d3-f5 (and thus prevent 2-move mate), then we have different solutions:

if 1... Nf2 (trying 2...Nf5) then 2. Ne3#
if 1... Ne3 (trying 2...Nd3) then again 2. Ne3#
if 1... Bb5 (trying 2...Bd3) then 2. Bb3#
if 1... f2 (trying 2... Qd3) then 2. Rf3#
if 1... Qf5 (trying e2 or e4) then 2. Rf5#

[Zag]

Sigh. I knew I couldn't possibly really get one right away. I'm not sure why I bothered to invis.

I'll try again at #1, using your hints.

1. Rb8 pinning the B on d8
if 1. .. Nxh6 2. Rc7#
if 1. .. Nd6 (or anywhere else) or Bf moves anywhere 2. Rf5#

edit: Now I've looked at MatthewV's solution, so I'm guessing I've missed something here, too.

edit 2: Maybe not. MV, you are vulnerable to Bb6+ 2. Rxb6+ is not checkmate, because he can still move Nd6

Also, Coyote, you neither accepted nor refuted lostdummy's solution for #2 (post 6). It looks good to me. (I know, that and a quarter will get you a newspaper.) Maybe you didn't see it?

[L'lanmal]

[MNOWAX]

ok, if thats the case...

#5 1: fRe5 this stops the queen from moving to d6 to stop the mate, so therefore...

if 1... Bb5, then Rc4++
if 1 ... Rd7 then Rd3 ++
if 1 ... Qxe5 then Rxe5 ++

i think i have this one. anyhtign i am missing?
_________________
The Man The Myth The Legend
MNOWAX

[Zag]

Here's my shot at #4.

1. Nc3 (to cover the a4 square if the queen is taken)
if 1. .. Bxc3 or Bxb3 2. Nd4#
if 1. .. Bg3 2. Nxg3#
if 1. .. Qf8 2. Nd6#
if 1. .. Nb6 2. Qxb6#
if 1. .. Nc7 2. Qb6#
if 1. .. Nxc3 2. Qb4#
if 1. .. Nb4 2. Aaaaaargh! I have no response to this!

Attempt #2.
1. Nb6
if 1. .. Bxb3 Ok. that approach fails right away.

Attempt #3.
1. Nd6 (to block Qf8 interfering)
if 1. .. Bxb3 2. Nc3#
if 1. .. Bf2 2. Ne3#
if 1. .. Bg3 2. Nf4#
if 1. .. Bh4 2. Nope

Attempt #4
1. Ng3
if 1. .. Bxg3 2. Nf4#
if 1. .. Bf2 or Bd2 2. Ne3#
if 1. .. Bc3 2. Nxc3#
if 1. .. Nb4 2 Nxb4#
if 1. .. Nc3 2. Nxc3#
if 1. .. Bxb3 2. Nc3#
if 1. .. Nb6 2. Nxb6#
if 1. .. Nc7 2. Nxc7#
if 1. .. Qf8 or Qd8 2. Ne7#

OMG, I think that's it!

edit: Oh no, I missed if 1. .. h6 oh crap

[MatthewV]

[lostdummy]

For #4, I think Zag shouldn't abandon his first attempt ;p

1. Nc3 , and then mate with Nf5-xx (or Qb3-xx in some cases)

if (copy all his cases), and also:
if 1.. Nb4 2. Qb4# (rook protect queen there)
if 1...Bd2 2. Ne3# (to prevent 2...Bg5)
if 1... g6 2. Ng7# (to stop black queen)
if 1... h6 2. Nh6# (to prevent black pawn taking white rook)

For #1, Zag's solution from post no.13 ( 1. Rb8 ) looks ok to me.

[Zag]

[lostdummy]

[L'lanmal]

[MatthewV]

[L'lanmal]

Since I don't see anything done on #5, I'll start the analysis by trying to find the sticking point of the puzzle.

Assume we move a rook, which seems safe given the theme. If we just move to a random square what responces does black have?

The most troublesome appears to be the knight move, as you can't seal off a knight, but if ...Nd1-f2 (or e3 or b2), then Nf1-e3#
If ...Ba4 moves, then Bg8-b3#
If ...Q-e4 or Q-e5 then RxQ. No problems there?
If ...e5 then RxP
If ...Rd7 then block it off with the other rook
The black squared bishop can't block a white diagonal.

Considering threats to the white queen, ...R-a6 appears blockable with either rook, and ...Q-d6 threatens both QxQ and Q-d3. This can be blocked by one rook on the 6th rank and one on the d-files. Or it can be pre-emptively blocked by R(either)-f4 or e5

So I have 3 classes of contenders for solutions: Rf4 or e5, rooks on e6 and d5 in either order, or rooks on d4 then f6. Not Rf6 first because PxR allows a pawn block. Oh, but if d5 and e6 both block the white bishop, so that's no good.

At this point, I'm wondering what defenses am I missing, and why is there a white pawn on h3.

If ...f2, then Rf4 or e3 would seem to work...
If g4xh3, then a rook to g4 or g5 is needed. Aha? This means Rf5-f4 is no good as a first move, but Re4-f4 is still a possibility.

Similarly If Rf5-e5, then the other rook can no longer block Ra6 with R-e6

What else?
(Current contenders: Re4-f4, Re4-e5 or Re4-d4.)

[MNOWAX]

sorry my latest post tahts spoilered is on #5
_________________
The Man The Myth The Legend
MNOWAX

[lostdummy]

my post no. 12 is also on #5 (and #2) - and I took advice from Coyote and didn't "spoil" it, , but I guess making problem numbers bold would help too ;p

[fadeblue]

For #5, I think Rd4 is the correct solution.

Re4-f4 is answered by f2.
Re4-e5 is answered by Rd7.
MNOWAX's suggestion of Rf5-e5 is answered by Ra6.

[Coyote]

Sorry I'm a little late here, but it looks like my input wasn't really needed anyway. There's not even much to add by way of commentary--you folks have been very thorough! Just a couple of brief notes:

#2. No one was fooled by the intended try by the rook. 1.Re5 also threatens 2.Qg7#, and now the replies to 1...Rg4 and 1...Rg2 are changed to 2.Nd4 and 2.Nd2. But 1...Be7 foils this attempt.
Incidentally this problem shows half battery combined with half pin: if either rook moves off the f-file, the other one is pinned. Half pin is a very popular idea amongst problem composers (maybe someday I'll post a set of problems centered around the idea.)

#5. L'lanmal did a pretty good job covering most of the false trails here. This is actually a much more complex example of the idea shown in the illustrative problem: random moves by the firing pieces are refuted by a particular black reply, and white has to find the right move to neutralize this reply. The full list is:

1. Either rook random--1...Qd7
1. Rf7 Pxf7
1. Rd6 Be8
1. fRe6 Ra6
1. fRf4 Pxh3
1. Re6 Bb5
1. eRe5 Rd7
1. eRf4 Pf2
1. Rd4 This one works!

Note that in all these cases except Rf7 the try fails because the rookk interferes with another white piece.

Well, that about wraps things up here. Thanks to everyone for your participation!