The 10 Highest-Rated Mate in 4 Puzzles

I recently downloaded the lichess puzzle database, which is a giant spreadsheet containing the position, moves, URL, rating, etc., of every lichess puzzle. I really like the Mate in 4 puzzles, so naturally I wanted to search the database for the 10 hardest ones! After finding them, I solved them all and wrote down my thoughts along the way. I recognized 7 of the 10 puzzles (I've done a lot of Mate in 4 puzzles) but didn't remember the actual moves to any of them!

First I'll provide direct links to the puzzles so you can solve them on your own if you want. Then in the next section I'll provide some commentary about each puzzle such as how I solved it, why I think it has a high rating, and what happened in the actual game. Finally, I'll conclude with some observations about the entire set.

The Puzzles

Here they are, starting with the highest-rated puzzle:

1. https://lichess.org/training/mxzcb
2. https://lichess.org/training/f0qUr
3. https://lichess.org/training/rpsSL
4. https://lichess.org/training/43cp9
5. https://lichess.org/training/NbvYl
6. https://lichess.org/training/VW1rY
7. https://lichess.org/training/ZHLHg
8. https://lichess.org/training/5V6Gv
9. https://lichess.org/training/tQBPV
10. https://lichess.org/training/9kyDi

Puzzle 1: The Highest-Rated Mate in 4 on Lichess! Rated 2941

What Makes It Hard?

I think the main thing responsible for this puzzle's high rating is the tempting but incorrect line where black wins white's rook. A lot of players probably see this and go for it - after all, they don't know that it's mate in 4! This is a good reminder of the classic rule: when you see a good move, look for a better one!

The puzzle took me several minutes even though I knew it was mate in 4, and even though I could reasonably assume that all of black's moves must be check (since white is threatening Rxf7+)! It's still hard because there are a lot of similar looking lines, for instance 1...Qh1+ 2. Kg4 Qh5+ 3. Kf4 Qg5+ 4. Kxe4 and white's king barely escapes. Or 1...Qh1+ 2. Kg4 h5+ 3. Kf4 Qc1+ 4. Kxe4 and once again white's king escapes.

Another thing that I think makes it tricky is that the move 2...Ne5+! allows three different responses from white but black must reply completely differently in each case. The three final mating positions are all completely different patterns which gives this one a nice study-like aesthetic.

How I Solved It

When I first saw the puzzle, I vaguely recognized it and remembered that I had previously gotten it correct, although I didn't remember the moves! Actually, I kind of misremembered that I was going to mate by bringing the black queen to c1 as in one of the lines above. A classic situation where remembering a little bit is actually worse than remembering nothing at all, as I got fixated on this idea and wasted some time.

What eventually led me to solve the puzzle was looking at the line 1...Qh1+ 2. Kg4 h5+ 3. Kf4 and wanting to be able to put my queen on f3 in that position. This caused me to seriously consider the ...Ne5+ sacrifice to get my knight out of the way.

What Happened in the Game?

The game continuation isn't that interesting, because both players had under 15 seconds. Black missed the mate and flagged :(

Puzzle 2, Rated 2903

What Makes it Hard?

In my opinion this one is just not hard and I'm disgusted by its high rating! I say this confidently because I remember solving it just a few days ago!

Ok, I'll try to say something useful. I'm positive that this puzzle's rating is high because everyone thinks it's easy and plays 1. Nf6+. The correct solution isn't that hard, it's just that people get tempted by this version of the idea that doesn't work.

Probably most people play way too quickly because they see 1. Nf6+ Kh8 2. Rd8+ Rxd8 3. Qxd8+ when black has to play 3...Rg8 and allow 4. Qxg8#. This is a common calculation error: when you're looking at a tactical/forcing line, you forget that the opponent doesn't have to capture. In the above variation, black can play 2...Rg8! and have a fine position. White doesn't even win material since black is threatening ...Qa1+ skewering white's king and rook.

If you saw the variation above and saw black's defensive idea, you can solve the puzzle by using the switching the move order calculation technique (I have a blog post about it!). Instead of starting with Nf6 and then checking on d8, check on d8 first, then on f6. This is a very common case where one order works and the other doesn't.

The correct first move, 1. Qd8+!, is also noteworthy. In the most common and intuitive kinds of sacrifices, the sacrifice is made and then the next move is a new check that wasn't possible before. But that's not what happens here! White seemingly sacrifices the queen for no reason, only to play a follow up check that was already possible on move 1. I've made up a term "out of order sacrifice" to describe this kind of move and have been collecting Mate in 4 puzzles that have them. I've noticed many of my students struggle to seriously consider sacrifices like this that don't create an immediate, new opportunity on the next move.

How I Solved It

I don't have anything useful to say because I saw the important details intuitively in a few seconds. I suspect I did actually look at 1. Nf6+ first and then immediately wondered about different move orders of the same idea.

What Happened in the Game?

White was rated 1600 and played 1. Nf6+ missing the mate. After some back and forth blundering white eventually won on time.

Puzzle 3, Rated 2894

What Makes it Hard?

Even though the first move is obvious, the second one is tough! 2...Qd4 is a great move and it's difficult to consider since it randomly puts the queen on an empty square where it can get taken. It's extra tough because you have to notice that ...Qd4 threatens two different mates so there's no easy defense, and a third mate appears if white plays 3. hxg4.

How I Solved It

When I looked at this one I remembered seeing it before and showing it to my student Bohan, who solved it much faster than me! I remembered it involved a queen sacrifice. Which again was probably not too helpful because it caused me to spend a lot of time looking at 1...h4+ 2. Kf3 Qxf4+. If white captures with the knight then 3...Nd4 is mate! But they can capture with the king instead when black has nothing. Eventually I considered 2...Qd4 just thinking that if they take that's an alternative way to get my c6 knight safely to d4. As soon as I seriously considered 2...Qd4 I realized it worked.

What Happened in the Game?

This one is fascinating! This was a 5 minute blitz game and the players were rated 1690 and 1688. Black thought for 20 seconds and played 1...Qxf4?!?! Objectively this move just blunders a queen, but in the game it worked! White thought for 2 seconds and played 2. Nxf4?? allowing mate after ...h4+ 3. Kf3 Nd4#. Really obvious lesson for the white player in this game who invested absolutely no time or energy trying to figure out the opponent's idea.

Puzzle 4, Rated 2861

What Makes it Hard?

Move 2 is hard to consider - it's a backwards move that hangs a rook and gives the enemy king more squares!

How I Solved It

I have a vivid memory of the first time I solved this one because it was during a class. Sometimes if I'm teaching a class and I find I haven't prepared enough material I'll have the students do some random mate in 4 puzzles. If my boss is reading this, that was just a joke, I'm always prepared! Anyway... the mate in 4 puzzles are usually easy for me and a good level for the students, but one time we got this puzzle. Eventually I solved it and was able to give everyone else a hint but the whole experience wasted at least 20 minutes of class time.

Black's king is stuck in a weird box with nowhere to go. When this happens it's really important to look for ways to threaten mate as it's possible one is unstoppable. When I just solved this puzzle again, I did so by noticing that in the position after 1. Re3+ Kf4, black's bishop is "overloaded" or "overworked," defending against Nd3 mate and Ng2 mate. Really the move 2. Re2! is the only way to turn either of those moves into a real threat by blocking the bishop! And of course if the bishop takes the rook, then the knight is free to play the other check on g2. I suppose it's a bit tricky, you have to appreciate that 3. Ng2+ still leads to mate even though you've sacrificed one rook and temporarily given black's king more squares.

What Happened in the Game?

White was rated 2285 and had 31 seconds on their clock in a 3+2 blitz game. White thought for 29 seconds, didn't find the mate, and forced a draw with Ref3+, Re3+, Ref3+, Re3+, etc.

Puzzle 5, Rated 2853

What Makes it Hard?

This is a good one! There are a lot of mate in 4 puzzles that involve a non-check move to threaten mate. But there aren't many where you threaten mate in 2. The point of 1. Kf5 is to control the g6 square so that white is threatening 2. Ng5+ Kh6 3. Rh8# It's a bit hard to believe that a mate in 4 puzzle can begin with a king move, especially one that allows the opponent an immediate check. But of course after 1...g6+ 2. Kf6 white still has the same threat!

I imagine a lot of people blunder in this puzzle with the tempting 1. Ng5+?? since they see 1...Kg6?? 2.Rxa6#. But there's no mate after 1...Kh6.

How I Solved It

I remember solving this one recently, I thought it was noteworthy and saved it in one of my lists of mate in 4 puzzles for students. The first move I considered was 1. Kh5 threatening the immediate 2. Ng5#. But 1. Kh5 doesn't work because of 1...g6+ and there's no way to maintain the threats. 1. Kf5 was the next move I looked at, just trying to find a different way to set up the same idea.

What Happened in the Game?

It was a time scramble between 1800's, five of the next seven turns were blunders, beginning with 1. Rxa6?? missing the mate. Then black played 1...d2?? allowing mate in 2 which white also missed.

Puzzle 6, Rated 2853 (again)

What Makes it Hard?

This one is tough! There are multiple candidate moves that threaten mate: ...Ne1, ...Kh6, and ...f6. To solve the puzzle you need to see that those don't work and look for something better. In particular 1...Ne1 is a tricky move, in the critical line shown above white has to find 2 only moves in a row and still must be very careful on the 3rd move. I'm sure a lot of people start calculating 1...Ne1 and then lazily play it because it looks so promising. I've noticed a lot of my students get really excited about threatening mate but are very reluctant to invest energy considering how the opponent may escape.

This puzzle is also another example of an "out of order" sacrifice. Black starts with the somewhat random 1...Bg5+, losing the bishop, just to follow up with 2...Ne1, threatening mate, which would have already threatened mate on move 1!

I think there's another insidious yet common calculation mistake that occurs in this puzzle, which is that you may begin by looking at checks, decide they don't work, and then forget to combine the checks you already discarded with other new ideas. This really slowed me down when I looked at the puzzle, I completely discarded 1...Bg5+ early on and it took me a long time to reconsider it in combination with the ...Ne1 idea.

How I Solved It

I remember solving this one somewhat recently before writing this blog, maybe a couple weeks ago. Despite that, I did not remember the solution. I don't have much useful to say about how I solved this one! I looked at all of the stuff above that does not work. Eventually I started looking at more and more random sequences and came up with the right one. When I noticed that 1...Bg5+ 2. Kxg5 Ne1 prevents 3. g4 (opening up g3 as an escape square, an idea featured heavily in the incorrect first move variations) because of 3...Nxf3# I realized that this was probably the solution.

What Happened in the Game?

Black was rated 1856 and it was a bullet game. Black played 1...g5+?? and lost. Any move for black besides 1...Bg5+! is completely losing since white has the easy plan of queening the a-pawn.

Puzzle 7, Rated 2812

What Makes it Hard?

To be honest, I don't understand the rating of this puzzle, and it's hard for me to figure out what makes it hard. Sometimes you just get lucky and look at the correct moves first, which is what happened to me with this one, so I'm out of touch with whatever other people are experiencing.

One guess is that in a lot of lichess puzzles the correct move is to just capture the opponent's material and then find some defensive moves. So people may be playing 1...Kxg7?? But the players rated high enough to get this puzzle will certainly see that this doesn't actually win material after the simple 2. Qb7+.

I think a better guess is that people see the line 1...Rxg4 2. fxg4 Qxg4+ with the idea of ...f3 next, setting up a mating net. But it doesn't work.

How I Solved It

This was the first puzzle I did not remember previously solving. Maybe it's a newer one? I looked at 1...Rxg4+ 2. fxg4 Qxg4+ but in my notes just wrote "seems like a dead end." I didn't even consider the idea of ...f3 next, which was dumb! But also somehow smart because it let me move on immediately to the correct solution! Next I tried 1...Rxg4+ 2. fxg4 f3+! and noticed 3. Kg1 Qxg4+ followed by 4...Qg2# and 3. Kf1 Qh3+ again followed by 4...Qg2#. I quickly saw that 3. Kxf3 Qh3+ 4. Ke2 Qxd3 is also mate.

What Happened in the Game?

Unfortunately, this tactic occurred in a time scramble like many of the others, so the fact that a 2647-rated International Master didn't find the mate isn't too surprising. Instead he played 1...Rxg4+ 2. fxg4 Qxg4+?? and then some random moves to flag his opponent.

Puzzle 8, Rated 2774

What Makes it Hard?

This one is not hard at all if you know it's mate in 4. It has a high rating because a lot of people probably instantly play 1...Rh8+, winning a knight with check after 2. Kg3 Qxh2+ but missing the forced mate. Remember, when you see a good move look for a better one.

How I Solved It

I too began by looking at 1...Rh8+ 2. Kg3 Qxh2+ 3. Kf3 Rh3+ 4. Ke4 but in this position I was aware that I was on move 4 and I didn't have mate in 1, so I knew this couldn't be it. I looked at some minor variations on this theme like 1...Rh8+ 2. Kg3 Qg1+ but they don't make a difference. Often, if you calculate an unclear line chasing the king across the board, you should look for a simpler way to "cut off," or restrict the king's path. This led me to consider 1...Qg1 which I quickly realized was the solution.

What Happened in the Game?

This was a 3+2 blitz game played between a 2448-rated FM and a 2498-rated untitled player. Black played 1...Rh8+?? but after 2. Kg3 Qxh2+ 3. Kf3 Rh3+ 4. Ke4 Qg2+ white played 5. Kd4?? instead of 5. Kf4 and allowed 5...Qd5#. In white's defense they had under 10 seconds for the entirety of this sequence.

Puzzle 9, Rated 2829

What Makes it Hard?

I think people get this puzzle wrong and inflate its rating for some of the reasons I explored in my blog about calculating discovered checks. White's first move is the most obvious, intuitive check, but then there's a discovered check, which means there are a lot of options and there are subtle differences between them. I bet a lot of players play 2. Rxd7+?? thinking the puzzle is about winning black's queen, forgetting that black can capture their own queen with 2...Bxb3.

How I Solved It

I don't have anything that useful to say, having recently written a blog about calculating discovered checks I certainly wasn't going to mess this one up! I quickly saw the line 1. Rf7+ Kh8 2. Ng6+ Kg8, realized I wanted my knight to come to f6 for checkmate, and that therefore I needed to play the discovered check 3. Re7+ to interfere with the black queen's control of f6.

What Happened in the Game?

Trust me, you don't even want to know. White was rated 1847, had almost 4 minutes on their clock, played 1. Rd2??, and then immediately resigned after 1...Bxb3 :(

Puzzle 10, Rated 2784

What Makes it Hard?

This one is difficult for very normal reasons: there are several possible checks on each turn, white has multiple ways to get out of check on turns 2 and 3, and the tree of variations quickly becomes large and overwhelming. There are some options for black like 2...Qh1+ that lead to mate against most white responses. If you're lazy and don't diligently examine all of white's options it will be easy to play one of these flawed variations.

Black's second move, 2...Qd1+, may be unintuitive for a lot of players since it sends the queen farther away from the white king. It's also not that forcing - white has three possible responses, all leading to slightly different mating patterns. And to me, it felt like after 3. Kf4 the white king is escaping into a bunch of open space. This puzzle definitely feels a bit "lucky" in the sense that the various final mates depend on arbitrary little details in the position, such as black's pawn on h6 controlling the g5 square and white's pawn on f6 taking a square away from the king.

How I Solved It

I distinctly remember once solving a position like this, with the queen zigzagging around, and thinking "wow this is weird." And then I remember the same thing happening again! To be honest, it probably happened many times before I caught on, but eventually I realized that this is a normal, typical pattern in open, attacking positions. Sometimes the queen will play several random looking checks only to return to its starting square to give mate!

Once I showed a puzzle like this to a group of kids and one of them said "it's like a boomerang," which I thought was funny, so that's how I've filed/remembered this motif in my own head since then. The first thing I wrote in my notes while solving this puzzle was "probably a boomerang." For me, realizing that these zigzagging queen checks are normal and then mentally labeling the theme has caused recognizing their possibility and solving the positions to become a lot easier!

Having said all that, solving this one was still a bit of a chore. There's no secret to how to do it, you just have to deliberately work through all the variations. But knowing the "boomerang" motif does make it a bit easier to consider strange checks. For example, one line I looked at and got excited about was 1...Qe4+ 2. Kg1 Qb1+!? 3. Kg2 Bf1+ 4. Kf3 Qe4#. Placing the queen on b1 may look weird but it's a typical kind of move in these positions. In this case it doesn't work because of 2. f3. I think I ultimately realized that after 1...Qf1+ 2. Kf3 Qd1+! I would have the strong option of 3...Qxd4 against 3. Kf4 which is necessary to mate.

What Happened in the Game?

It was another silly time scramble, black gave a bunch of random checks, didn't accomplish anything, and flagged :(

Final Observations & Conclusion

I'll conclude with some observations about what difficult features appeared in multiple puzzles.

A Tempting But Wrong Option

Sometimes a puzzle isn't hard because the correct solution is particularly difficult, but rather because there is a shorter, easier, or more obvious answer that turns out to be wrong. In my opinion, this is the biggest factor driving the high rating of these puzzles, and clearly applies to:

• Puzzle 1: Black can win a rook for free and fail the puzzle
• Puzzle 2: People play 1. Nf6+ which looks good but isn't because of a later, hard to see detail
• Puzzle 6: There are so many ways to threaten mate, I imagine most people fail the puzzle by playing one that doesn't work
• Puzzle 8: Black can win a free knight with check and fail the puzzle
• Puzzle 9: White can win black's queen and fail the puzzle

I also think it's also possibly relevant to:

• Puzzle 5: 1. Ng5+ is somewhat tempting, obviously leading to mate in one variation
• Puzzle 7: This was the puzzle that confused me the most, but it was somewhat difficult to see why the variation that threatens mate with ...Qxg4+ and ...f3 didn't work

Unintuitive Sacrifices

In my opinion, 5 of the puzzles involve sacrifices that I would describe as "unintuitive." When I solved these puzzles, I looked at a lot of other options first before eventually considering these moves.

In my commentary above I mentioned the idea of an "out of order" sacrifice. This clearly happens in:

• Puzzle 2: white sacrifices the queen, then plays a follow up check that was already available on move 1
• Puzzle 6: black sacrifices a bishop and then plays a move to threaten mate that already would've threatened mate on move 1

For me these kinds of sacrifices take a lot of mental effort to seriously consider. Compare these to puzzle 7 which relies on very typical, intuitive sacrifices: black's first move sacrifices a rook, but enables a new check on move 2. That move is also a sacrifice that, when accepted, allows the black queen to enter the position on a previously protected square. Each move is enabled by the previous move. This is very typical and the logic is easy to follow.

Another notable thing about the sacrifices in puzzles 2 and 6 is that they involve moving a piece to an empty square. This is often more difficult to consider than a sacrifice that captures a piece. This is also seen in:

• Puzzle 1: ...Ne5+ is a hard move to consider since the knight moves to an empty square where it can get taken

At least the three sacrifices above were all check! Maybe even harder to find were:

• Puzzle 3: Black's queen is attacked, so it moves to a different empty square where it can get taken, and it's not even check
• Puzzle 4: White plays a backwards rook move to an empty square that is not check, and in the process of letting the rook get captured even gives the enemy king more squares

Of course, we should consider these moves, because they threaten mate! Which leads to the next topic:

Checks vs. Mate Threats

Generally I believe that it's easier and more intuitive for most players to calculate sequences of checks rather than mate threats. It often takes more mental effort to figure out how the opponent will respond to a mate threat, and these threats often don't accomplish anything. In this set of puzzles, half of the puzzles were all checks and half of the puzzles involved a mate threat. To be honest I would've guessed that more of the puzzles would involve mate threats, and I was particularly surprised that the two highest-rated puzzles were solvable with only checks. But I'm also certain that if we looked at lower-rated Mate in 4 puzzles a smaller percentage would involve any non-check moves. Maybe my next blog will be on the 10 lowest-rated mate in 4 puzzles (just kidding, I looked and they're all back-rank mate!).

Large Tree of Variations

Difficult positions are often difficult because they have many appealing options, many possible opponent responses, etc. It's hard for me to accurately assess how this affects the difficultly of these puzzles for a few reasons. In some I may have gotten lucky by looking at the correct moves first, causing me to underestimate the number of reasonable candidate moves. I also recognized a lot of the positions and although I didn't remember the solutions, I may have approached them differently the first time I saw them. It's hard to know.

I can safely say having many options, or a "large tree," caused the following puzzles to be difficult:

• Puzzle 1: Tons of possible checks on every move and multiple possible responses!
• Puzzle 6: Many very appealing ways to threaten mate, also a few checks to calculate
• Puzzle 9: There are a couple checks in the starting position, then the discovered check means that there are many similar yet different checks on move 2
• Puzzle 10: A classic example, there are multiple checks available on every turn and white has multiple options against most of them

It may also play a role for:

• Puzzle 4: There are a few different ways to threaten mate before or after 1. Re3+
• Puzzle 7: For the last time, I really don't understand this puzzle, but I guess people get sucked into looking at checks, captures, and threats that don't work out, like 2...Qxg4+

Notable puzzles with a small tree of variations are:

• Puzzle 2: There aren't many checks or threats to look at
• Puzzle 8: There are only two ideas in the position, win the knight or trap the king

Conclusion

After going through all 10 puzzles, I think the main takeaway is that their difficulty is mostly dependent on: how many reasonable options there are, and how easy/intuitive it is to even consider the best moves in the first place.

Another obvious conclusion is that the puzzle ratings are somewhat meaningless when you know it's mate in 4. Knowing there's a forced mate allows you to ignore many of the otherwise tempting options like winning material.

A more personal observation, but I found it pretty weird the way I remembered 7 of the 10 positions, sometimes including information like when I solved them or who I solved them with, yet I didn't remember any of the solutions! This definitely made me think that I should be doing some kind of additional self-reflection after each puzzle to really cement the idea into my mind, though I'm not sure what that process would look like.

Overall I really enjoyed doing these puzzles and will get to work on numbers 11-20 next!