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Bad puzzles

Puzzle 7874 is bad.
1. ... Re8+ 2. Qe2 Rxe2+ 3. Kxe2 is correct. But next 3. ... bxc3? 4. bxc3 Ba6+ 5. Ke1 Qb6? 6. Kd1 ... is bad.
http://ru.lichess.org/training/7874
The best combination: 3. ... Ba6+ 4. Ke1 Qe3+ 5. Kd1 Be2+ 6. Ke1 Bxf3+ 7. Kf1 Qe2+ 8. Kg1 Qg2#
Am I mistaken?
You are correct. 3...bxc3 throws away the forced mate, and then 5.Qb6 also misses a forced mate. Just a bad solution.

I've noticed quite a few puzzles like this where either the answer is clearly wrong. I know there are limited resources here, so it may not be feasible, but it would be nice if the training problems were engine-checked.

A related minor complaint of mine is about the gap between the content of the training and the title of "training".

Many of the puzzles start from a position where one side is completely winning, and has many absolutely crushing moves, but one is perhaps a little better than the others.

I understand those sorts of things in composition/study style puzzles, but I'm not so fond of them as "training", since if I'm up a queen, a rook, and a piece, a move that is +15 and simplifies the position may well be a better move in a game than a move that is +20 because of complicated tactics. Both win, and one is much less prone to miscalculation.

For training purposes, it would be best if the initial positions were not obviously winning for one side, and if there were only one solution.

Having said that, I know that these features are all implemented on a best-effort basis, and having such tools available for free is fantastic. Just my two cents of constructive feedback. :)
bishop, I think you're correct. I tried the puzzle before reading, and I came to the same conclusion. A forced mate should be treated as better than winning material.
Hi, puzzle 3666 looks wrong after 1.g4 Nxf4 both 2.Qxf4 and 2.Nxf4 should be accepted since i see no reason to prefer one on the other. I played Qxf4 and get it wrong :o

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