Chess Problem Solutions

Mate in 2

1.	Rhg7
1.	...	Kc8	1.	...	Ke8	1.	...	Nb7	1.	...	Nf7	1.	...	Ne8	1.	...	Nc8
2.	Ra8#		2.	Rg8#		2.	Ra8#		2.	Rg8#		2.	Ra8#		2.	Rg8#

Mate in 2

1.	Re1
1.	...	Kxe1	1.	...	Bg2	1.	...	B~
2.	Qd2#		2.	Qh4#		2.	Qg1#

Mate in 2

1.	Rg4
1.	...	Kc1	1.	...	Kb3	1.	...	Kd3	1.	...	B~
2.	Rc4#		2.	Qxd1#		2.	Qe4#		2.	Qb1#

Mate in 3

1.	Bb8	f2
2.	Rc7	Kh2
3.	Rh7#

Mate in 3

1.	Nd5		(threatening 2. Nc7#)
1.	...	Rg7		1.	...	a4	1.	...	Rc6
2.	Rb6#			2.	Nc7+	Ka5	2.	Rb6+	Rxb6
				3.	Rb5#		3.	Nc7#

Mate in 3

1.	g8=N	b5
2.	Ne7	Kxb4
3.	Nc6#

Mate in 4

1.	Kf5	Kd6
2.	Ne4+	Kxd5
3.	Kf6	Kxe4
4.	Bc6#

Mate in 5

1.	Ba3	b4
2.	Bbd4	bxa3
3.	Ba1	a2
4.	Kc3	Kxa1
5.	Kc2#

Mate in 6

1.	Bd1		(threatening 2. Bb3#)
1.	...	Kc4
2.	Bb3+	Kd3
3.	Ba4		(threatening 4. Bb5#)
3.	...	Kc4
4.	Bb5+	Kd5
5.	Nf3		(threatening 6. Re5#)
5.	...	Kxe6
6.	Bc4#

DON'T mate

1.	c4+	Rxc4
2.	e4+	Rxe4
3.	Ne7+	Rxe7
4.	Nc7+	Rxc7	stalemate

Selfmate in 5

1.	Ba6	ab
2.	Bb5	bc
3.	Bc4	cd
4.	Bd3	de
5.	Be2	ef#

Selfmate in 2

1.	Re5	Kf7 or Kh7
2.	g8=R	f2# or h2#

Selfmate in 3

1.	Ra4	c6
2.	Ra5	c5
3.	c4	g4#

Win

1.	c7	Rd6+
2.	Kb5	Rd5+	(if 2. Kb7 Rd7, and if 2. Kc5 Rd1 3. c8=Q Rc1+)
3.	Kb4	Rd4+
4.	Kc3	Rd1
5.	Kc2	Rd4
6.	c8=R	Ra4	(if 6. c8=Q Rd4+ 7. Qxd4 stalemate)
7.	Kb3		(threatening both 8. Kxa4 and 8. Rc1#)
	1 - 0

Win

1.	Be3+	Kb7
2.	e7	Rxa3
3.	Ba7	Ra1
4.	Kf4	Rf1+
5.	Bf2	Rxf2+
6.	Ke3	Rf1
7.	Ke2		(and the pawn promotes)
	1 - 0

Win

1.	Bh6+	Kg8
2.	g7
2.	...	e5	2.	...	e6	2.	...	Kf7
3.	Ke6	e4	3.	Kd6	Kf7	3.	g8=Q+	Kxg8
4.	Kf6	e3	4.	Ke5	Kg8	4.	Ke6	Kh8
5.	Bxe3		5.	Kf6		5.	Kf7	e6/e5
	1 - 0			1 - 0		6.	Bg7#

Draw

1.	Kg7	h4
2.	Kf6
2.	...	h3	2.	...	Kb6
3.	Ke6	h2	3.	Ke5
3.	c7	Kb7	3.	...	h3	3.	...	Kxc6
4.	Kd7		4.	Kd6	h2	4.	Kf4	h3
	½ - ½		4.	c7		4.	Kg3
				½ - ½			½ - ½

Draw

1.	f7	Rf8
2.	e6	b6
3.	Kb7	Kc5	(if 3. e7 Rxf7 and the e-pawn is pinned)
4.	e7	Rxf7
5.	Ka6	Rxe7	stalemate

Draw

1.	Rf8+	Kd7
2.	Rf7+	Ke6
3.	Rf5
	½ - ½

If black moves away his attacked rook he loses the other one with Rf6+, and if his king retreats to the 7th rank white checks as before.

Find the Last Move

1.	Nb6	Ka7
2.	Na8+	Kxa8

Where is the White King?

Answer: c3

1.	Kb3	Bd5+
2.	c4	dc+
3.	Kxc3+

On which Square was the White Queen Captured?

Answer: h6

Proof

First consider which white pieces were captured on e6 and h6. The bishops never moved (look at the pawns), so it must have been the queen and the missing knight.
Next consider which black piece was captured on b3. Only the bishops are missing, and so it must have been the white-squared bishop.
Finally consider the order in which these captures occurred. The first capture must have been the white knight on either e6 or h6. But if it was on h6, how could the white-squared bishop get out to b3? So it must have been e6, and therefore the white queen must have fallen on h6.

After Black's 4th Move

rnbqkb1r/ppp2ppp/8/8/8/8/PPPPPPPP/RNBQKB1R

1.	Nf3	e5
2.	Nxe5	Ne7
3.	Nxd7	Nc6
4.	Nxb8	Nxb8

After Black's 4th Move

rnbqkbnr/pp3ppp/2p1p3/8/4P3/8/PPPP1PPP/RNBQK1NR

1.	e4	e6
2.	Bb5	Ke7
3.	Bxd7	c6
4.	Be8	Kxe8

After White's 16th Move

1.	Nc3	d5
2.	Nxd5	g6
3.	Nxe7	Nf6
4.	Nxg6	Ne4
5.	Nxh8	Nc3
6.	Nxf7	Qg5
7.	Nxg5	Nb1
8.	Nxh7	Bd7

9.	Nxf8	c6
10.	Nxd7	b5
11.	Nxb8	Kf7
12.	Nxc6	Kg6
13.	Nxa7	Kh5
14.	Nxb5	Ra3
15.	Nxa3	Kh4
16.	Nxb1

Thorny Construction Task

r2q3B/1pp2pp1/2p1p3/8/1P4PP/4PP1b/3PRQNk/1B2BKR1

Proof Game

1.	Nf3	Nf6
2.	Ne5	Nd5
3.	Ng6	Nb4
4.	Nxf8	Nxa2
5.	Ng6	Nb4
6.	Ne5	o-o
7.	g3	Nd3+
8.	cd	a5
9.	b4	a4
10.	Nc3	a3

11.	Bb2	a2
12.	Rc1	a1=Q
13.	Bh3	Na6
14.	Be6	Nc5
15.	Nf3	Qa5
16.	Ba2	Ne4
17.	de	Qf5
18.	ef	Ra6
19.	h4	Rg6
20.	fg	Re8

21.	gh+	Kf8
22.	h8=B	Kg8
23.	Kf1	Kh7
24.	Kg1	Kg6
25.	Nd5	Kh5
26.	Bd4	Kg4
27.	Nh2+	Kh3
28.	f3	Rf8
29.	Ne3	Re8
30.	Ng2	Rf8

31.	Bf2	Re8
32.	Qf1	Rf8
33.	e3	Re8
34.	Re1	Rf8
35.	Re2	Re8
36.	Be1	Rf8
37.	Qf2	Re8
38.	Kf1	Rf8
39.	Rg1	Re8
40.	Ng4	Rf8

41.	Ne5	Kh2
42.	Nc6	dc
43.	Bb3	Bh3
44.	g4	Qd7
45.	Ba2	Ra8
46.	Bb1	Qd8

Description

The wBh8 requires wPc2xd3xe4xf5xg6xh7-h8=B, consuming all missing black units except black-squared bBf8. Then the bPa7 had to be promoted before it can be captured. So that a wP (a or b) had to be captured to open the way (and no 2nd white promotion is possible). The other missing white unit is a wN, captured by d7xNc6. bPh7 cannot have been promoted, so that it has been captured at home.

The S-E corner unlocks by (1) retracting wPg3-g4, then (2) extracting the bBh3, then (3) retracting bKh3-h2, then (4) inserting something on h2 and (5) retracting Rh1-g1. Then everything unlocks. But only a wN can reach h2 for step (4). This wN must be resurrected on c6, after bBc8 is driven back home (requiring that e7-e6 is taken back).

Now we see that the bK had to leave the 8th rank before d7xc6 or e7-e6 took place. He had to go through the h7 hole, when there was a promoted wBh8. Necessarily, the bKR was still there (so that the bQR has been captured) and it could only let the bK out if the first move of the bK was O-O. (The bR now on a8 is the original bKR, the bKB was captured at home, the wPa2 was captured on its file).

Checkmate after Black's 5th Move Promoting to a Knight

rnbqkbnr/pppp1ppp/8/8/8/1P6/PKP2PPP/RNBn1BNR

1.	d4	e5
2.	Kd2	ed
3.	b3	d3
4.	Kc3	de
5.	Kb2	exd1=N#

Stalemate after White's 10th Move

5bnr/4p1pq/4Qpkr/7p/7P/4P3/PPPP1PP1/RNB1KBNR

1.	e3	a5
2.	Qh5	Ra6
3.	Qxa5	h5
4.	Qxc7	Rah6
5.	h4	f6
6.	Qxd7+	Kf7
7.	Qxb7	Qd3
8.	Qxb8	Qh7
9.	Qxc8	Kg6
10.	Qe6		stalemate