## Tuesday, August 12, 2014

### Checkmate in 5

White to move and checkmate in 5.

Puzzle by Kovalenko, presented by Andreas

6R1/6P1/8/8/8/K7/6P1/kr6 w - - 0 1

Marshall Lusk said...

Ra8 seems like an option. Am I right?

Anonymous said...

Do you mean mate in 6

PROF.S.G.BHAT said...

Interesting puzzle.
It is sure white should first move the R,but to which square.Let us solve algebraically.Let it move to "y" file where y could be c,d,e,f or h.What is black's defence?If R moves on file say 1.... Rb7, white plays 2.Ry1+ Rb1 3.g8=Q followed by mate at a2. So black will move R on the first rank say to file "z" where z could be c,d,e,f or h but different from y.2nd move white queens, black plays ...Rz3+ .3rd move white plays 3.Qb3.now we have to look for two possiblities (1) R taking the Q Then 4.Kxb3 Kb1 Now on 5th move white should mate by R by 5.Ry1#.This eliminates file c from the list of y.Now y=d,e,f,h are left.
(2)Black does not take Q but mate is threatened on first rank.So black plays 3.... Ry3 preventing check by white R.White is forced to take R by Q only 4.QxRy3 otherwise there is stalemate.Black plays 4... Kb1. This is possible if b1 is not controlle by Q at y3.Ths means d file is not y file.So now y=e,f,h are left.Now the 5th move must be mate.This is possible by Q check on first rank but Q should control c2 also.this means y3 from where Q is coming must be nothing other than f3.
So we have the solution.
1.Rf8 Re1
2.g8=Q Re3+
3.Qb3 Rf3

(3.... Rxb3+ 4.Kxb3 kb1 5.Rf1#)
4.Qxf3 Kb1
5.Qd1#

Harry Hariharan said...

1.Rf8!
>A-1...Rc/d/e/h1.2.g8=Q!. Rc/d/e/h3+. 3.Qb3!.Rxb3+.4.Kxb3.Kb1.5.Rf1#
eg
1. Rf8 Rc1
2. g8=Q Rc3+
3. Qb3 Rxb3+
4. Kxb3 Kb1
5. Rf1+

>B-1...Rf1.2.Rxf1#
>C-1...Rg1.2.g8=Q!.
>>C1-2....Rxg2.3.Rf1#
>>C2-2....Kb1.3.Rc8!.Rxg2.4.Qb3+.Ka1 or Rb2. 5.Qd1# (if 3....any other move 4.Qa2#)

>D-1...Rb3+.2.Kxb3.Kb1.3.Rc8.Ka1.4.Rc1#
>E-1...Rb2/4/5/6/7/8.2.Rf1+.Rb1. 3.g8=Q!.any 4.Qa2#

It seems that 1.Rd/e/f/h8 also mates in 5!

Harry

Anonymous said...

Ra8 !

PROF.S.G.BHAT said...

Actually it is mate in 9::5 by white and 4 by black.

Harry Hariharan said...

No, mate in 5!

Harry

Yancey Ward said...

A better question for this puzzle is not really to find the 1st move, but to explain why that move allows a mate in 5 where other similar moves are moves in 6 or more. The difference is very subtle, and I literally didn't understand it until I reached the end (and I almost overlooked the mating move, too!)

A hard puzzle. What makes it difficult for me is that there isn't any clearly obvious reason one rook move along the 8th rank might be better (by a move or two) than another. Let's look at my first wrong choice, since it can help illustrate why the solution is the shortest mate possible:

1. Rc8

Threatens g8Q, of course. I had no particular reason for choosing this square for the rook, I just needed a way to get my teeth into the problem. Now, the black rook can leave the 1st rank, but white will mate in 4 total moves: [1. ...Rb6 2.Rc1 Rb1 3.g8Q Rc1 4.Qa2#]. So, black must move the rook along the 1st rank, and he must move the rook to a square where he can check safely on the 3rd rank on the next move- these moves are Re1 and Rd1

1. ......Re1

Now, here for white, my plan was to guard the 3rd rank with the rook:

2. Rc3

Now, black's rook can't leave the 1st rank unless he pins the rook with Re3, but it is mate in 5 total moves if black does play Re3. However, if black returns the rook to b1.....

2. ......Rb1
3. g8Q Rb3 (shorter #s else)
4. Kb3

Both Rxb3 and Qxb3 are stalemates. Continuing:

4. ......Kb1

And white can only mate by move 6. Nor can white do better at move 2 the line above by queening the pawn:

2. g8Q Re3
3. Qb3

This is the shortest mate I can find in this variation, but it doesn't solve the problem. Continuing:

3. ......Rb3
4. Kb3 Kb1

And, again, white mates in 6 total moves.

Even after this, I still didn't really see the solution, but let's look at my next choice which is the actual solution, and I will tie it back into the variation above:

1. Rf8!

Again, the threat is g8Q followed by Qa2#. As before, the black rook can't leave the 1st rank without allowing a mate in 4 moves total. Now, lets look at the lateral moves along the 1st rank, starting with the same Re1 as in the previous line:

1. ......Re1

Threatens Re3+, however....

2. g8Q Re3

Or [2. ...Kb1 3.Qa2 Kc1 4.Qb2 Kd1 5.Rc8#], and, of course, 2. ...Re6 loses quickly to Rf1+ followed by Rxe1#. Continuing:

3. Qb3! Rf3

If 3. ...Rxb3, then 4.Kxb3 is followed by 5.Rf1#. Any other move along the 3rd rank also is mate in 5. Continuing:

4. Qf3! Kb1
5. Qd1#

And right there is your difference- the queen can reach d1 from f3 without also stalemating the black king by taking b1 away at the 4th move as she would from b3 and especially from d3.

Now, who could see that at the beginning? If you can, you are better at this than I am.