If White doesn't play the puzzle move, he's slightly behind in material, and needs to play passively to defend d4. But if he does play it and Black declines, then

29 Rxf4+ Kg6
30 R(f)e4

leaves him slightly ahead in material with a dangerous attack.

Just for a test ride, I copied and pasted the diagram, as well as the busy Stockfish output, using the analysis line feature from the new chess viewer.

click for larger view

29...Kg7 30. Rxg5+ Kh8 31. d5 c5 32. c4

This is one way although 32. c3 also traps the N

click for larger view

Now it is impossible to avoid mate or loss of the N

29...Kg7 30.R:g5+ Kh8 31.Qe1 Qd6 32.Rh4 Rg8 33.Qe4 Qc7 34.R:g8+ K:g8 35.Qe6+ Kf8 36.Qf6+

29. Rxf4+ Kg7
30. Rfe4 Qd6
31. Qxg5+ Kh8
32. Re8+ Rxe8
33. Rxe8+ Qf8
34. Rxf8#

it's clear from the comments from middling players (including myself in that tribe) that an "easy" position for one player can be "difficult" for another.

we all have a peculiar way of looking at the board, and computer chess analysis is exactly that -- chess without the human element.

i usually ignore comments that merely post a computer analysis, because i am a human player and am interested in what other human players found important or trivial in a position.

it's fine when world class players choose lines that match a computer analysis; they're world class players. but there is a large difference between finding the computationally "correct" line and playing as a human being.

comments such as "easier than tuesday" suggest the editors of chessgames.com should eliminate the difficulty scoring and simply present the puzzles of probably increasing difficulty, the way the NY Times used to publish crossword puzzles (which, though most difficult on sunday, did not come with a difficulty score).

for the rest of us, we see the board with a directional bias, as if illuminated by a flashlight, leaving other parts of the situation completely dark.

30.Rfe4 succumbs to ...h6

Good points. The "world class" players don't always follow computer lines. They might in fairly clear positions but often don't in the middle game. Sometimes they seem to play slightly "inferior" moves even in the opening as they prefer the positions arising.

Of course they do sometimes follow the computer lines or suggestions. Of course that requires a good memory.

In endings and simpler positions or typical positions I think they usually find the "computer" move.

It is obviously best to analyse without a computer for most of us though as the computer doesn't tell us why moves are played.

Solving these (Monday, Tuesday, Wednesday) is fairly easy depending on (sometimes the type of position or tactic is recognized). It gets harder as it progresses in the week, but the simpler ones are good to practice with. Going through the tactics examples even just dialing up what was played helps with tactical training. This is a good method before a game or tournament.