I tried to treat these positions as if I was playing a 3-min game, so I didn't take a ton of time to calculate. Just sort of played intuitively.

1) Got it pretty much right away
2) Same, saw the tactic pretty quick
3) Wanted to play Be3 quickly because it feels natural, but I didn't see the Qxb2 Bd4 idea right away. That's nice.
4) Didn't really get any points because I didn't calculate everything. I saw the sacs and how open white's king was and just went with it.
5) Saw the Rd8 idea, but kept wanting to somehow force mate. Your solution about gaining space and pushing back white's king is really nice. I like it more than a tactic because it's not as obvious but really shows an understanding of the position. Well done.

Thanks for posting, I enjoyed going through these.

Are you kidding? Either I'm way weaker than 1400, or the quiz is not for 1400s, or it's rather for slow or corr games! I was mostly clueless about the solutions!

1) I don't see a clearly good move, but I guess that the king penetration 1... Ra7 (to prevent White's rook from going to b7) and 2... Kg5/h5 is good. Time = 10 min.

2) 1... b3 2. axb3 a2, 2. Rd1 b2 with a tremendous protected passer. 3 min.

3) 1. Nc3 (threatening d6 - the e-pawn is now pinned) Qd6 2. Nb5; 1... Kd8 just strips Black of the castling rights. 3 min.

4) 1... Qf8, threatening a discovered attack Bd2+, but that threat is easily defendable... well, I guess the best move is not always a crushing tactic - I see none here. 6 min.

5) I guess you meant 1... Rd8 (threatening f6#), but 2. f5 Rd6 is not really crushing for Black. 4 min, 26 min total.

Now I'll calculate the score...

1) Oh dear, I was thinking about 1... Rab8, but didn't see 2... Ra8.

4) Holy cow, I didn't even see 1... Bxe5.

5) I did see 2... f6+, but didn't think that it was the solution because it merely throws the White king back. I'll award myself half a point for that, ending with 1.5/5

1) 1. Qa4+ N8c6/N4c6 2. d5, 2. Qxb4 to any other Black's reply.

1 point if you found the entire tactic.

2) 1. Rxd7! Kxd7? 2. Bxc6+! bxc6 3. g4 Qh3 (Qg6 4. Ne5+) 4. Ne5+ Kc8 (Kd6/Ke6 5. Qxc6+ Kxe5 6. f4#) 5. Qa6+ Kd8 6. Qxc6 Qxg4 7. Qd5+ Ke8 8. Qxa8+ Qc8 9. Qxc8#.

6 points if you found the entire combination, including the optimal mating attack after 3... Qh3. 5 points if you saw the 3. g4 Qg6 4. Ne5+ fork and either found a mating attack after 3... Qh3, but only a slower one (in its longest line; e.g. 5. Qxc6 instead of 5. Qa6+; not finding the mate in 2 after 4... Kd6/Ke6 is a separate case awarding 4 points, see below), or missed some of Black's best defences (like 4... Kc8), or found 1. Rxd7 but opted to play 2. g4, which also crushes after 2... Qh3 3. Bxc6+ and so on, but a bit slower. 4 points if you found the 3. g4 Qg6 4. Ne5+ fork and the general direction of the mating attack after 3... Qh3, but failed to consider 4... Kd6/Ke6 separately or find mate in 2 there.

3) 1. Bxc6 Bxc6 2. Qxc6 bxc6 3. Ne7+.

2 points if you found the entire tactic. 1 point if you chose to play 1. Bxc6 Bxc6 2. Ne7+? Kf8 3. Nxc6/Qh4.

4) 1... Nxd4 2. Qxd4 Nh5.

1 point if you found both Black's moves. -1 point if you played 1... Nxd4 2. Qxd4 e5? like myself in the game (the d-pawn is pinned to the queen, so 3. Bxe5 wins the e-pawn for nothing).

5) 1... Ng4! 2. h3 Qf2+ 3. Kh1 Nxe3 4. Qxe3/Rxe3 Qxc2 (or Bxd5 5. exd5 Qxc2).

2. fxg4?? Qf2+ 3. Kh1 Qf1+ 4. Rxf1 Rxf1#, as in the game

2. R3e2? Qxh2+ 3. Kf1 Qh1+ 4. Qg1 Nh2+ 5. Kf2 Rxf3+ 6. gxf3 Qxf3#.

2. Ne7+!? Kf8! 3. Qh8+!? (Nxg6+ hxg6 4. Qxd6+ Kg8 5. Qg3 Qxg3 6. hxg3 Nxe3) Kxe7 4. Qxa8?? Qxh2+ 5. Kf1 Bc4+ 5. Rd3 Bxd3+ 6. cxd3 Rxf3+ 7. Ke2 Qxg2+ 8. Kd1 Rxd3+ 9. Kc1 Qd2+ 10. Kb1 Qxe1+ 11. Kc2 Qd1#.

5 points if you figured out how to respond optimally to all the listed White's 2nd moves. 4 points if you failed to consider the fancy 2. Ne7+ 'defence' or find the crushing response Kf8 to it, but found a forced mate in the 2. R3e2 line and figured out how to reply to both other feasible second-move defences listed above. 3 points if you failed to consider the 2. R3e2 line or mate optimally there, but found the mate in 3 after 2. fxg4.

Myself, I scored only 5/15 in the games (i.e. the rapid chess mode): 1, 0, 2, -1, 3. I was contemplating Rxd7 as a tactical sac just for the lols in 2) when playing, but of course wouldn't have found g4 that fast. Here are my White game and my Black one.

For #3, Nc3 with the idea you have in mind is good too. Full point for that.

Yeah, >1400 is too low. Kind of biased into thinking they weren't that hard because I got them in blitz games.

I spoiled myself on your quiz after waking up 4 hours too early, a state during which I do irrational things, and now I regret that.

1) 1... Nxd4 2. Be3 b5 3. Bxb5 Nxb5. (3. Bb3 Nxb3.) 2. Qxd4 Nh5 as before. Note that Bb3, which would grab the exchange, has to be prevented, hence the b5 move (to exchange the LSB off while the knight is still on d4).

2) 1... Ng4 2. h3 Nxe3 3. Rxe3 b5 4. Nc3 c6 5. Nb5 c5.

2. Ne7+!? Kf8 3. Qh8+!? Kxe7 4. Qxa8?? Bc4 5. h3 (fxg4 Qf2+ 6. Kh1 Qf1+) Qf2+ 6. Kh1 Bf1. This faster mate has become available because Qa8xb7 is no longer with check.

2. fxg4?? Qf2+ 3. Kh1 Qf1+ as above. 2. R3e2? Qxh2+ 3. Kf1 Qh1+ 4. Qg1 Nh2+ 5. Kf2 Rxf3+ 6. gxf3 Qxf3# as before.

I don't get this one, 1...Nxd4 2. Be3?? seems to lose a piece to any reasonable Black move: 2...Nc6, 2...Ne6, 2...e5. Black has plenty of cover for the e6 square after White donated his knight.

second one I kind of want to play 1...Rxf3, but Ng4 looks clearer

Damn, you're right, those responses are all viable. The engine suggestion 2... b5 is only like 0.1 ahead of 2... e5 - the reason why it likes b5 is that Black regains the pawn by playing Rb8 (attacking whatever piece is on b5) and Rxb2, thus spoiling White's pawn structure.

In the second position, 1... Rxf3 2. gxf3 Nxf3+?? fails because, after 3. Rxf3 Qxe1+ 4. Rf1, Black has to give up the queen because White is threatening Ne7#. 4... Qh4 doesn't help either because, after 5. Nf6+, Black has to still sac the queen at some point to prevent mate, e.g. if he doesn't do so now, the king will have to walk into a nasty discovered check, and White's attack is apparently pretty dangerous.

So the best follow-up is 2... Qxe1+ 3. Rxe1 Nxf3+ 4. Kh1 Nxe3 5. Nxc7 Rc8 6. Nxe6 Nxe6 7. Nc3, and Black ends up with equal material and chances, not winning.

yeah I was intending 2...Qxe1+ but I agree there is not much there. Maybe Black could start with 1...c6 intending 2. Ndc3 Rxf3

19.Qc2 g6 20.Bxg6 hxg6 21.Nxg6+ 1-0
Perhaps a premature resignation in a game between low rated players, but again there are multiple ways to win.

In my online correspondence game, I played 1. Qe7+ and premoved 1. ... Kg8 2. Nf6+ Kh8 3. Qf8+ Qxf8 {3. ... Rg8 4. Qxg8+ Qxg8 5. Rxg8#} 4. Rxf8+ Rg8 5. Rxg8# Can't resist that queen sac! Frustratingly (but fairly) the opponent resigned after Qe7 and deprived me of my sacrificial pleasure. Over the board I would play 1. Rxe8+ Kxe8 2. Qe7# every time. There are of course also many other ways to do it.

Qe7+ ... Kg8
Qxe8#

Question: Why would you do all those superfluous moves? Do you hate the guy you are playing? Seems unsportsmanlike imo. Not that I'm judging - I'm often unsportsmanlike.

The reason why I played them is because I liked the aesthetic of the queen sacrifice and mate in the corner. I agree it's a little bit unsportsmanlike, which is why I would NOT do it over the board, and probably not in a live game online either. To me, though, a lot of the unsportsmanlike aspect of it is the wasting of time, and because premove allows me to negate that in the correspondence setting, I decided to go with it (feeling slightly bad about it as I did so... but doing it anyway).

The differences of opinion on the sportsmanship aspect are precisely why I classified it as a psychological question

1. Rxf7+, etc.

This mate is prettier than the 5. Rxg8# line, largely because it isn't gratuitous.