Hopeless position

Logic Level 5

Take a look at the position below.

With optimal play from both sides, does white have a forced mate? If so, in how many moves?

(If he doesn't have a forced mate, give 0 as your answer)

NOTE: This is a very difficult problem


The answer is 203.

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1 solution

Seth-Riley Adams
May 16, 2016

Relevant wiki: Chess Puzzles

White has a forced checkmate in 203:

Walter Jörgensen, Die Schwalbe 1976

---Annotations by John Nunn--- http://en.chessbase.com/post/longest-dual-free-direct-mate-problem

White to play and mate in 203 moves We immediately see that due to the material superiority of the opponent White cannot win by conventional means. He must execute a forced mating attack. The first task, however, is to blockade the black pawn on h3 and gain total control of the position. So let us begin: 1.Qg1+ Kf3 2.Qf1+ Kg4 (2... Ke4 3.Qd3 mate) 3.Qe2+ Rf3 4.Qe6+ Rf5 5.Bh2 With the introductory moves White has tied down the position so that the opponent's forces can no longer be mobilized. We take note that Black cannot move either of his knights: if he moves the Ng6 then White mates immediately with Ne5; the move 5...N8e7 allows 6.Qe2+ Rf3 7.Qe4+ Rf4 8.Nf6#; 5...Nf6? just delay the end by one move: 6.Nxf6+ Kf3 7.Qe3+ Kg2 8.Qg1+ Kf3 9.Qf1#. There is only one continuation for Black: 5...Kf3 . This threatens to release the black heavy pieces, which White must avoid at all costs. 6.Qe3+ Kg2 7.Qg1+ Kf3 8.Qf1+ Kg4 9.Qe2+ Rf3 10.Qe6+ Rf5 . We will call these five moves the "Jörgensen Manoeuvre". They have led to the position after White's fifth move (see diagram above), but with White to move. What can White do with the free move? If Black had no pawns on the a and c-files the game would soon be over: White executes the Jörgensen Manoeuvre three times, bringing his king to d1 in the process, after which Black cannot play ...Kf3 any more, because Qe2 would be mate. He has to move a knight which leads to mate as described above. You may think that White could simply go after the black pawns after each Jörgensen Manoeuvre, but note that moving the king to a4 leaves it open to a rook check when the black king moves to f3; and playing c3-c4 will make the white king vulnerable to rook checks on the third rank, which it could thus no longer occupy. No, the process is much longer and more convoluted. 11.Kb2 Kf3 12.Qe3+ Kg2 13.Qg1+ Kf3 14.Qf1+ Kg4 15.Qe2+ Rf3 16.Qe6+ Rf5 17.Kc1 Kf3 18.Qe3+ Kg2 19.Qg1+ Kf3 20.Qf1+ Kg4 21.Qe2+ Rf3 22.Qe6+ Rf5 23.Kd1 Now Black must move a pawn (23...Kf3? 24.Qe2#) 23...a4 . This offers the greatest resistance. 24.Kc1 24.Ke1? allows the a-pawn to promote. 24...Kf3 25.Qe3+ Kg2 26.Qg1+ Kf3 27.Qf1+ Kg4 28.Qe2+ Rf3 29.Qe6+ Rf5 30.Kd1 a5 . After 30...a3? 31.Kc1, 37.Kb1, 43.Ka2, 49.Kxa3, 55.Kb2, 61.Kc1 White can make three king moves without the Jörgensen Manoeuver (67.Kd1 a5 68.Ke1! a4 69.Kd1) saving a total of ten moves. 31.Kc1 Kf3 32.Qe3+ Kg2 33.Qg1+ Kf3 34.Qf1+ Kg4 35.Qe2+ Rf3 36.Qe6+ Rf5 37.Kd1 a6 38.Kc1 Kf3 39.Qe3+ Kg2 40.Qg1+ Kf3 41.Qf1+ Kg4 42.Qe2+ Rf3 43.Qe6+ Rf5 44.Kd1 a3. The first "lemming suicide plunge": the black pawn has had to move to a square on which it can be safely captured – after four Jörgensen Manoeuvres: 45.Kc1 ... 51.Kb1 ... 57.Ka2 ... 63.Kxa3 . Now the white king must return to d1 to force another pawn move: 69.Kb2 ... 75.Kc1 ... 81.Kd1 a4. Now White uses the Jörgensen Manoeuvre to shuffle his king between c1 and d1, forcing black pawn moves: 82.Kc1 ... 88.Kd1 a5 89.Kc1 ... 95.Kd1 c4 . Note that after the next Jörgensen, 96.Kc1 Kf3 97.Qe3+ Kg2 98.Qg1+ Kf3 99.Qf1+ ... ... Black can try 99...Ke4, since White can no longer mate with Qd3. But 100.d3+ does the job: 100...Kd5 (100...Ke3 101.Bg1+ Rf2 102.Qxf2#) 101.Qxf5+ Ne5 102.Qxe5#. So: 99...Kg4 100.Qe2+ Rf3 101.Qe6+ Rf5 102.Kd1 c5 103.Kc1 Kf3 104.Qe3+ Kg2 105.Qg1+ Kf3 106.Qf1+ Kg4 [106...Ke4? Black can try to use the free c6 square by 106...Ke4?, but this proves in vain after 107.d3+ Kd5 108.Qxf5+ Kc6 109.Qe6+ Kb7 110.Qb6+ Kc8 111.Qc7#.]. 107.Qe2+ Rf3 108.Qe6+ Rf5 White still cannot pick up the pawn on a4: 109.Kb2? Kf3 110.Qe3+ Kg2 111.Qg1+ Kf3 112.Qf1+ Kg4 113.Qe2+ Rf3 114.Qe6+ Rf5 115.Ka3 Kf3 116.Qe3+ Kg2 117.Qg1+ Kf3 118.Qf1+ Kg4 119.Qe2+ Rf3 120.Qe6+ Rf5 121.Kxa4 Kf3 122.Qe3+ Kg2 123.Qg1+ Kf3 124.Qf1+ Ke4! 125.Qe1= (125.Qxc4+ Kf3-+ The queen is pinned!; 125.d3 Ke3–+). 109.Kd1 a3 110.Kc1 ... 116.Kb1 Kf3 117.Qe3+ Kg2 118.Qg1+ Kf3 119.Qf1+ Ke4! This forces White to capture the pawn on c4, giving the pawn c5 an extra move. 120.Qxc4+ [120.d3+? Ke3!–+] 120...Kf3 121.Qf1+ Kg4 122.Qe2+ Rf3 123.Qe6+ Rf5 124.Ka2 ... 130.Kxa3 ... 136.Kb2 ... 142.Kc1 ... 148.Kd1 a4 149.Kc1 ... 155.Kd1 c4 156.Kc1 ... 162.Kd1 a3 163.Kc1 ... 169.Kb1 ... 175.Ka2 ... 181.Kxa3 ... 187.Kb2 Kf3 188.Qe3+ Kg2 189.Qg1+ Kf3 190.Qf1+ Ke4. Black extends the solution by two moves. 191.Qxc4+ Kf3 192.Qf1+ Kg4 193.Qe2+ Rf3 194.Qe6+ Rf5 195.Kc1 Kf3 196.Qe3+. The Jörgensen Manoeuvre is executed for the last time. 196...Kg2 197.Qg1+ Kf3 198.Qf1+ Kg4 199.Qe2+ Rf3 200.Qe6+ Rf5 201.Kd1 The final zugzwang. 201...N8e7 [201...Kf3 202.Qe2#] 202.Nf6+ Kf3 203.Qe2#.

This was by far the hardest logic puzzle, I guess, after seeing the solution.
By the way, is there any proof that this is minimum and you literally expected people to make 203 logical moves? Just asking, I dont have any solution for this and to be very honest i didnt even read your whole solution.

Yatin Khanna - 5 years ago

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It would have taken extra time to write the logical solution to solve this problem. So here's a link to the full solution here: http://en.chessbase.com/post/longest-dual-free-direct-mate-problem. I will update the solution shortly with explanations​.

Seth-Riley Adams - 5 years ago

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It will require at least 5 hours to understand then, i suppose. Anyways, my vacations are on and i will try my best...

Yatin Khanna - 5 years ago

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@Yatin Khanna Hehe :D. Good luck!

Seth-Riley Adams - 5 years ago

I mistakenly believed I had a chance to solve this puzzle. ...I am glad that I gave up. Wow. Just wow. Who came up with this? I imagine a grand master staring at this position for like 5 hours and then looking up at his opponent and saying "Mate in 203. You lose". At the very least, it's an extremely impressive puzzle. I feel like there should be some kind of warning :P

Alex Li - 5 years ago

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Hehe :) I think I'll give a little warning...

Seth-Riley Adams - 5 years ago

Oh my God!

Such a difficult question. I think it must be rated as level 10. ¨ \Large \ddot\smile

Samara Simha Reddy - 5 years ago

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Haha! I thought it should have been rated at Level 6 :D

Seth-Riley Adams - 5 years ago

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I think you are damn good at Chess!

Samara Simha Reddy - 5 years ago

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@Samara Simha Reddy Well...I'm not bad...

Seth-Riley Adams - 5 years ago

What's wrong with White Queen to g1- check. Black King has only one move that is to f3. White Queen to g3-checkmate. 2 moves

reg caton - 3 years, 3 months ago

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After Qg1+ Kf3 Qg3+ the Black king can either go to e4 or e2.

Seth-Riley Adams - 3 years, 3 months ago

1 pending report

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