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Why should I take the rook on C5 rather than on D2 here?

It's probably because after Nxd2, White can play Rb5 and win the b4 pawn. It's still winning, but according to the engine, it's a "pawn" worse
Based on the local evaluation , the rook on c5 can swing over and attack your b pawn, whereas the rook on d2 isn't really attacking anything.
6.5 -> 5.7
totally winning position -> totally winning position

there are a lot of broken puzzles like this
i m sure developers will find a way to improve them :3
#thibaulttheboss
#4 it's more like:

totally winning position -> slightly suboptimal but still totally winning position

The puzzles are generated by engine analysis, and so whatever the engine has selected as the best line during the analysis is going to be the best move. The fact that taking the other rook is slightly worse evaluation but not quite an inaccuracy is why it gives the "good move, but you can do better" dialogue and doesn't punish you for the move. However, 6.5 is objectively better than 5.7 and the point of the puzzle is to find the *best* continuation. Therefore it is not "broken" it is simply not how a traditional constructed puzzle works.

The SIMPLE answer as requested by the OP as to why can be explained just by looking at it positionally:

After Nxb2 how are you continuing your attack? Where is the knight going? How are the rooks working to attack the king? White's main idea here is to cut the king off from climbing back up to rank 3. There is absolutely no chance of doing this after Nxb2 and there are really no good forcing moves. However, after Nxc5 it cuts the e4 and d3 squares off from the king, so he can't run away because of Rhe1+ followed by Rbc1 threatening mate in 2. So the SIMPLE answer is that after Nxc5 Black's pieces are still well coordinated, but after Nxb2 Black will have to reposition pieces and White has some initiative to try to generate counterplay, even though he is still lost.

Fenris1066 sir, let me explain myself
"Which rook does knight capture (and black totally crushes white anyway)??" is not the question of the puzzle. (Good) Puzzles should contain only one way to victory, once the decisive advantage is gained, the rest doesn't matter.

Nuances of which rook to capture is totally irrelevant.
This is a 1172 rated puzzle, and it's purpose is "not to directly fork the rooks" and "to play ...Rh1+ firstly to fork rooks+king so white can't play Rc8+ inbetween move to save the rooks"
**Preventing inbetween move with a forcing move (check) to win clean material advantage**
I'll agree Usolando that the idea for an 1172-rated puzzle should simply be to win the rook, and it shouldn't much matter which. In this case, if you take one, you get a "good move, but you can do better" and then you take the other and win. It isn't like you fail for taking the other rook.

Objectively, taking either rook wins. Subjectively, taking one rook leads to a much more coherent positional win than the other. So what I'm saying is that it isn't "broken" because positionally, the solution is better than taking the other rook. It's also not "broken" because if you take the other rook, you don't fail the puzzle. You are simply guided that while that still wins, maybe the other rook is better to take for some reason.

The OP was asking why. Unlike many others, I actually told him why. It has to do with positional nuance. Understanding that nuance isn't required to win the puzzle, as choosing the other position doesn't outright lose the puzzle. Looking at these things is necessary for solving tougher puzzles, however, because maybe in a future puzzle, not looking at the position might yield failure because taking that rook might actually give the opponent more significant material back or even allow them a winning tactic. You should ALWAYS evaluate the position before choosing between 2 apparently equal opportunities, because sometimes one is not as equal as it looks. This puzzle subtly teaches that very important lesson without exacting any penalty, and so I think that's a good thing!

If anything, I think that while this is a good puzzle, it may be rated too low due to the nuances of the tactic and the positional ideas after. I really don't understand how the ratings are determined.
@Fenris1066, regarding puzzle ratings (which you also mentioned in passing in some other thread) I might be wrong, but from my understanding, it is an indirect application of glicko-2. With the usual ratings, we have player vs player with the player with the higher rating getting penalized more for losing (or drawing) and gaining less for winning and the one with the lower rating getting reverse treatment. The larger the disparity between player ratings, the greater this rewards/punishments are.

With puzzle ratings, we have player vs puzzle instead. You win against a puzzle and that puzzle's rating will go down and your rating will tend to go up (and vice-versa). Now, the weakness to this non-direct setup is that since there aren't any puzzle vs puzzle conflicts (which isn't really going to happen if you think about it), I gather that the fluctuations/inaccuracies are even more pronounced.

By the way, it seems that there are 60,120 puzzles. (If you try visiting puzzle 60121 or beyond, you get a 404 page which has that mini-game scroller which I stopped trying to play when I realized how it can potentially shorten the lifespan of my mouse button.)

P.S. This c5/d2 rook question is like Morpheus asking Neo to choose between the blue and red pills. :3
If that's truly how the puzzles are rated, that makes sense I guess. But if only high rated players are playing the stronger puzzles, those ratings will go down and it will take awhile for them to go back up as people like me fail them. So it seems like the fluctuation could be pretty wide, especially for puzzles that don't come up much. But I don't really know a better way to do it.
Would it maybe be a good idea if you would get (or could choose to get) chess puzzles that were mostly upvoted by other players that mostly upvote and downvote the same puzzles as you do? Similar to StumbleUpon, but for chess puzzles.

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