insane HeXO puzzle

Added: 2026-05-25

[00:00:00]Hexo is a game where you and your opponent take turns placing two pieces at a time. Whoever connects six pieces in a row first wins. Here is the puzzle.

[00:00:08]It is X's turn to play. Yes, this position came from an actual game. No, I don't know how they managed to end up in this position. There is a way to force a win in 34 moves. Normally, I would tell you to pause and try to find the forced win yourself, but this puzzle took me nearly 10 hours, so I wouldn't recommend it. That being said, the fact that this puzzle is a forced win in 34 moves is not particularly impressive. Due to the board being infinitely large, it is possible to engineer puzzles with arbitrarily long forcing winds. The interesting part of this puzzle is the fact that there even exists a forced win. The position looks remarkably even, and you probably don't even know who has the advantage, let alone who can force a win. It's X's turn to move, but they're under threat. If they don't block this threat, they will lose. So, one of X's pieces must go to waste, and it is impossible to even create a threat with their other move. This means that O can make quite literally any move in response. And if we want to find a forced win for X, we need to account for all of these cases and make sure that X can force a win in every single scenario. With that being said, X does indeed have the forced win. Here is how.

[00:01:12]X's first move is to block the threat like this and go here. But that doesn't make much sense out of context. Why is this move a good move? To explain that, it is a better idea to forget about the puzzle for now and focus on the position. What about this position is advantageous for X.

[00:01:29]After a bit of testing, you might stumble upon this move. This creates a double threat. O must use both of their pieces to block, otherwise they will lose. Now that O has used up their entire turn, it's our turn again. So, we can make another double threat. But O simply blocks again, and we aren't really accomplishing anything. So, how about we create a four in a row, which is another double threat. O must block on both sides, otherwise they will lose.

[00:01:53]Now it's our turn again. We create another double threat. O blocks. We do it again. O blocks again. We do it again. O blocks again. And now we can create two double threats at the same time. O cannot block all four threats with only two pieces. So, X wins.

[00:02:07]Now, it looks like X just forced a win here. But let's take a step back. First of all, here is the puzzle again. We want to play this move in order to force a win. But unfortunately, O has a threat here, so this doesn't actually work as a solution to the puzzle. You're going to lose. Also, I was being a bit misleading. O blocked this double threat by going here and here, which is suboptimal. Blocking here would be better. If you try the same thing as before, O blocks here and here. Yes, this defense still works because there's not enough space to create six in a row.

[00:02:36]The point of making this very specific move is to line up the defending pieces.

[00:02:40]When you make this double threat, O again lines up their defending pieces.

[00:02:44]Now when you try to make this double threat, O can block and simultaneously create a threat of their own. Now you have to go block that and you can't force a win anymore. There is no way to avoid this. O is always able to form these lines of three which prevent you from making a double threat without getting handed one in return. The bottom line is O is always able to defend this position by going here and here. They can also defend by going here and here.

[00:03:07]That's also an option. In fact, this defense is better because it doesn't even require O to make a line of three at all. You can do whatever you want and still defend.

[00:03:16]Now, it looks like we're at a dead end, but this will be very useful information later on. When X makes this move, which we'll call attack A, O only has two very specific ways to defend. We're going to call this one the inner defense and this one the outer defense. If they choose the outer defense, they must also block the next double threat in a very specific way. Great. Now, we're going to put that away for now and move on. Of course, by move on, I mean go back to the exact same question we were trying to answer. What about this position is advantageous for X. After some testing, you might find this move, which we'll call attack B. This is not a double threat like attack A was. In fact, attack A is the only way you can make a double threat. Attack B is only a single threat, which is obviously not as strong. O only needs one piece to block, and their other piece can go wherever they would like it to go. But we now have two preemptives which we can turn into double threats whenever we want.

[00:04:09]Additionally, we have created what is called a closed three. There's also another closed three down here. We can turn a closed three into a single threat using just one move. What's more, this can create another closed three. So, we can use our second piece to create another single threat. This is now a double threat, and O must spend their entire move blocking it. So, we can just create another double threat in the same way. And we can do this for as long as we'd like. However, again, O just keeps blocking, and again, we're not getting anywhere. The winning move here is quite tricky to find. It is to make this slightly different double threat, which forfeits our ability to keep making double threats in return for two preemptives right next to one another, which is very powerful. This will actually lead to a forced win. But there are three different ways to defend this double threat and also three different ways that O can defend the next double threat, and so on. How can we be sure that X can force a win in all of these scenarios? The solution is just to consider all three scenarios at once.

[00:05:05]Let O use all three of their defenses at the same time. Of course, this can't happen in a real game, but this is just for the sake of the proof.

[00:05:20]Notice that in this position, O does not have any threats on the board, even though this is the best possible scenario for O. So, this means that O won't be able to make a defensive threat no matter what they do. So X is free to make this move which creates both a double threat and a single threat. O cannot defend this triple threat with only two pieces and X wins. This has a very important implication. Let me go back to the original position. When X makes this move, which we called attack B, O not only needs to block this single threat, they also need to do something about this closed three down here.

[00:05:52]Because if they don't, they're going to lose in the way we just outlined. So O must use up their entire turn. one piece to block the threat and the second piece to block down here. And now it's X's turn again. Since the closed three on the bottom led to a win, maybe the closed three up here will also lead to a win. Unfortunately, let me go to another spot since we're running out of space here. Nothing works. This attack looks promising because you create two preemptives, but unfortunately they both point towards the same spot. If you turn one of the preemptives into a double threat, the other one becomes useless.

[00:06:23]You can't turn it into a double threat anymore. This is only a single threat, which gives O enough enough leeway to defend. So, this attack doesn't work.

[00:06:30]How about this one? Oh, wait. This is basically the same thing as attack A, which we already analyzed. There are two possible defenses, the inner one and the outer one. Either one of which O can use to fully defend. So, it looks like once again we are at a dead end. But there is a very clever forced win here. Can you find it?

[00:06:51]The solution is to start with this preemptive, turn it into a double threat. O is going to defend by blocking on the left and right. And we are going to pay close attention to how they block on the left. If they block like this, they are now susceptible to this attack.

[00:07:05]Remember that the only reason O could defend this attack was because these two preemptives both point to the same spot.

[00:07:11]And since O didn't block that spot, this preemptive isn't useless anymore and it can be turned into a forced twin. But what if O chooses to block the normal way? This attack won't work anymore. X needs to try something different. The answer is this move. Attack A. Remember that attack A has two possible defenses.

[00:07:29]The inner defense and the outer defense.

[00:07:31]Notice how the outer defense requires this double threat to be blocked like this. Otherwise, O will not be able to defend. Well, guess what? O has already inadvertently messed up the defense.

[00:07:41]First of all, you can't do inner defense anymore because this piece down here is in the wrong spot. It should be here for inner defense, but it's not. So O is forced to do outer defense, but that fails because outer defense requires this piece to be here in order to line up the defending pieces. Without there being a line of three, O cannot defend, and X is able to force a win. Now, you may have already spotted a flaw in this plan. Let's go back to the beginning. X makes attack B. O must defend the single threat and also defend the bottom. X makes a double threat. O defends. And now, apparently, we need to go here to win. But this is only one move. Where is our other move going to go? Ideally, we would want our second move to make some sort of threat. Maybe we find a closed three somewhere on the board. And using our second move, we turn it into a single threat. That combined with our single threat over here would make a double threat and leave our opponent with no leeway at all. But if you look around the board, there isn't a closed three anywhere. We need to make one first before we can make this attack and force a win. Good thing we still have this move. Attack B. O needs to block this single threat and also block down here. This leaves a closed three up here, which is exactly what we want. Now we just turn this into a threat. Go back and make the move we wanted to, thereby making another threat. And O needs to block both of these threats. And now we can force a win. You already know how to force a win for attack A. The other winning sequence, this one, is left as an exercise to the watcher. So now we have found a forced win for this scenario, which we'll call scenario A.

[00:09:09]We know for sure that X can win from this point on. But consider this. What if earlier O chose to block here instead? We'll call this scenario B.

[00:09:17]This is very slightly different from the old scenario A, which I'll indicate here in green. If we try making the same attack as before, O blocks like this.

[00:09:26]Our next move, according to our earlier plan, should be to go here as well as make a filler move. In scenario A, O was forced to do outer defense. But in this new scenario B, inner defense becomes available. And inner defense works all the time. It doesn't require there to be a line of three, so you can no longer force a win. So, how do we counter this?

[00:09:44]How can we force a win in scenario B?

[00:09:48]The solution turns out to be one of the most satisfying sequence of moves I have ever seen. First, we're going to create another scenario B, a duplicate. All we need to do is go somewhere else and use attack B. Recall that O must block the single threat, then block the closed three on the bottom. This leaves us with scenario B up here. So, now we have two identical scenario B's basically. Now we are going to use both scenarios at the same time. One piece will go to each ladder, each piece making a threat. O must block both threats and they must block on the top instead of the bottom because blocking on the bottom would turn this into scenario A which we already know to be a forced win for X.

[00:10:24]So they must block on the top like this.

[00:10:26]And now we will just do the exact same thing again. We're climbing up the ladder one step at a time. They block again and we do it one more time. And now we make this move. O is forced to activate inner defense twice. And now we no longer need two scenario B's. So we are going to focus solely on one of them. Here is the fourth win.

[00:11:06]The logic behind all of these moves needs some explaining. So, let me control Z 50 times. Also, we should prove that this winning sequence does work no matter how O defends. All right, here we go. This first double threat is there to open up this preemptive. Then we use that preemptive to obtain an X here. This will be important soon. Our next move is to use this preemptive down here. It is tempting to make this double threat because it looks like all the action is on the left. So, we should position our pieces accordingly.

[00:11:32]However, the fatal weakness of scenario B is this open corridor right here. So, we actually go to the right so that we can grab this spot. Then, we activate the preemptive down here so that we can build up an attack through the corridor.

[00:11:46]Now, it is time to put those two pieces up here to use. We can create a double threat by going here and here. Now, we have a closed three through the open corridor and we use it to place an X inside the spot. This spot will become very important later. First though, we must continue the attack downwards by creating these two preemptives.

[00:12:05]We can create a double threat here that creates this closed three. And notice how these two closed threes both converge on the same spot. We take that spot thereby making a double threat. And our second piece makes it a triple threat which is impossible to defend with two pieces. If you look around the position, you will find that there is not a single four in a row for O. They could not make a defensive threat even though this was the best possible scenario for them. So they will lose no matter what.

[00:12:30]Now we aren't actually done with the puzzle yet. Even though we have proved that X can win both scenarios A and B and therefore attack B is winning for X in the actual puzzle we're under threat.

[00:12:41]If we make attack B, we will lose. So now it's time to go all the way back to the beginning where I said that X's first move should be this. Why is this a good move? Well, let's say O defends up here. Notice that we have this closed three right here, which we can use to force a win. Remember when we first analyzed attack B, we realized that O needed to defend the bottom. Basically the same thing is going on over here. So O needs to defend this closed three somehow. All right, let's say O defends it with both pieces. Now X can win with this preemptive up here.

[00:13:19]So it turns out O needs to defend both the closed three and the preemptive. And now it's X's turn again and we make attack B and win using it. That is the entire puzzle. I hope you enjoyed it. If you'd like to know where I got the puzzle from, it originated as an image that was sent in the Hexo Discord. And a few minutes after that image was sent, someone else sent the message, "X can force a win here, right?" You know, maybe they figured this all out within a few minutes. Somehow I kind of doubt it