Puzzle

I think this shows that the idea of first promoting white's a-pawn completely using Ra8 as well does not work, because underpromoting to the rook is not possible without check.

I PM'ed a solution, but I see a partial solution has been posted. In my PM, the game viewer did not work properly, so here is a corrected version.

Bf1 never left home, so Ba2 is promoted. Pb3 didn't come from a2, because Ba2 never could have gotten there if it did. The a2 pawn cannot be any of the other pawns on the board, so it must be the one that promoted, required 6 captures on light squares. The remaining missing black unit is Bf8, which must have been cap'ed on e3.

Because all of black's units are required to have been captured, g7 must have promoted to reach a suitable sacrificial square. It must have captured its way to b2, since d2/f2 would have checked wK and spoiled white's castling. This accounts for the fate of all white's missing pieces.

Retracting moves from the diagram shows that white needs to use the f-pawn for tempi when he has no other retractions.

If the pawn were at f3, wRh1 could not have come out to be sacrificed. So, the pawn must be on f6 in the diagram.

Good stuff. I didn't see the Bc1 block check idea.

That was the weirdest game ever.

Problem 2:

Light first rope at one end and second rope at both ends.

The second rope will burn out after 30 minutes. At this point, light the second end of the first rope.

The first rope will burn out after a total of 45 (30 + 15) minutes.