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A wonderful new chess problem has appeared lately that is most wonderful. I am here to share it with the world today. But you must solve it in order know about it’s glory!

It’s White to move and mate in four.

Peter Hoffmann, berlinthema.com, 12/8/19

enter image description here

May you solve it first and appreciate it’s beauty!

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The setup and mate in four immediately reminded me of

the Babson Task

Since Black is threatening

1... Qxh2+ which at least delays mate by a couple of moves,

White's first move must be

1. Bxg1

Black now has

some moves with the knight and king, which I haven't analyzed but assume they'll lead to unthematic mates.

The problem is really about

the different promotions by the black e-pawn:

First:

1... e1Q 2. axb8Q threatening all kinds of mate-in-twos, e.g. a discovered check from the queen on f8, or 3. Na6 Kxd5 4. Be4.
Some lines:
(A) 2... Qxe7 3. d7 Qd6 4. Qfxd6#
(B) 2... Qe5 3. Qa7+ Kxd6 4. fxe5#
(C) 2... Qxc3 3. Re4 Qxc1 4. d7#

Second:

1... e1R. Now 2. axb8Q Rxe7! delays the mate long enough, since 3. d7 (from line A) is now stalemate.
Promotion to rook doesn't help; 2. axb8R Re5 and Qa7 from line B is not available.
But promotion to bishop helps: 2. axb8B! Re5 3. Ba7+!

Third:

1... e1B. Now 2. axb8Q Bxc3 3. Re4 (line C) is stalemate, as it would be when White promotes to rook or bishop on move 2.
However, 2. axb8N works: bishop moves are met by 3. N8a6+ and 2... Kb6 by 3. Nd7+ Ka5 4. Qa8# (or 3... Ka7 4. Ra1#).

Final:

1... e1N. Now 2. axb8Q fails because 2... Nxd3 3. Bxd3 is stalemate.
By promoting to a rook, 2. axb8R Nxd3 3. Bxd3 Black can take on d6: 3... Kxd6 4. Rf7#.

So this is related to what Tim Krabbé calls a

cyclic Babson (also referred to in the title of this puzzle)
but not quite; here the promotions to queen do match each other. So:
if Black promotes to a queen, White promotes to a queen;
if Black promotes to a rook, White promotes to a bishop;
if Black promotes to a bishop, White promotes to a knight;
if Black promotes to a knight, White promotes to a rook.

A wonderful puzzle! (Even though capturing a piece on the key move, a queen no less, is usually considered bad form.)

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  • $\begingroup$ This is the 9th realized possible cycle: it has been a decade the last realized cycle. Congratulations on solving! I'll award you here in awhile. How'd you solve it? $\endgroup$ – Rewan Demontay Dec 9 '19 at 13:48
  • $\begingroup$ The key move is rather obvious, and then Black's four main defenses are kind of obvious (if you know about these types of chess problems). White's second move is also the same as in the first 'perfect' problem of this type, the one by Yarosh published in August 1983. $\endgroup$ – Glorfindel Dec 9 '19 at 13:52

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