Posted 20th Jun 2026 at 16:32Greetings all

I love Hanjies, so much so that Dr. Moore rolls his eyes every time he sees an email from me. "Yes, yes, I know, more Hanjies!"

Anyway, he's going to give us a bunch over the next week and it's been a while since I posted my guide to solving Hanjies for those who haven't done them before.

First, let me specify my terminology.
Row: Line going left to right.
Column: Line going top to bottom.
Square: Each individual chunk of a Hanjie.
Square Number: The square using the row counted from the left then the column down from the top. Top left is 1:1. Top right on a 20x20 is 20:1. Bottom left is 1:20. Bottom right is 20x20.
Marked Square: Square marked with the dark color to denote a part of the picture.
Null Square: Square marked with the light color to denote a square that's not part of the picture.
Block: Each individual number listed to the left or top to denote a sequence of marked squares. This can be 1 to any number up to the full length of a row or column.
Bridging: Technique where you mark the center squares of a row or column that must be marked. I'll explain this below.
Paperwork: Technique where you keep track of what you've done. I'll explain this below.

I'm going to start with nothing. As in null squares. Marking squares as definitely not marked is perhaps the most powerful tool in your arsenal. If you can look at the Acropolis 40x40 puzzle in the Travel Collection, you see an amazing example of this.

I'll explain how I can determine this when I get to bridging, but the squares at 25:11 (25 left to right, 11 down) and 25:15 both must be marked. As you eliminate the easy stuff at the bottom of this puzzle you're left at one point with the column only having the blocks 5, 1, and 1 remaining from the top. Now, as I say, 2 squares are definitely marked by going across on the 11 and 15 rows.

This leads to a incredibly useful conclusion that the square at 25:16 must be null. How? Because you know the 5 block is the top remaining one on that column. The squares at 25:11 and 25:15 are separated by 3 squares, meaning there's a chance the block of 5 is those 5 squares. If that's the case, then the square at 25:16 is null as the bottom marker of that block. However, if the 5 is higher on the column, then the block at 25:15 must be a 1, meaning again that the square at 25:16 is null for the same reason.

So, we mark it as a null. In this game, this is perhaps the single most important thing you can do, because if you look at Row 16, you see it has these blocks: 10, 13, 1, 1, 3. That null at 25:16 breaks the row up. If you count from the right, you have the 3 block, a 1 block, and another 1 block, which leaves only 7 squares to the right of the null square at 25:16, so the 13 block has to be to the left of it.

In this case, then, we now know that both the 10 block and 13 block must be to the left, but it turns out those fit exactly. 10 marked squares, a null square, 13 marked squares, and that gets us exactly to the 25:16 square.

Basically, marking that one null square at 25:16 gets you two large blocks that you definitely know are there. This is a great illustration of the power of null squares to subdivide a Hanjie. If you're stuck, mark every null square you can figure out and see where that leaves you.

The next thing I'll talk about is "bridging." This is my term for adding marked squares based on the middle part of a block that the row or column demands must be marked. That's a cumbersome way to explain it, so I'll give you an example.

First, you reserve spaces for all the blocks on a row or column. If you have 20, 4 row on a 40x40, then you reserve 4 squares plus an empty square to the right, and then you count the bridge to the left. In this case, that leaves a 20 block to fit in 35 squares. If you count from left and right on the subdivided row, you see that the 20 block must occupy the squares 16-20.

Up above provides a better example. I talked about the Acropolis puzzle using Row 11. In this case, Row 11 a 40 square row with the following blocks: 27, 1, 1, 1, 1, 1. Ok, so let's count this out from the right.making sure we allow enough space for all the smaller numbers. So 1 block, space, another 1 block, space, another 1 block, space, another 1 block, space, and now the final 1 block and one more space. That means the minimum amount of space these 5 1 blocks consume is the first 10 squares. They could easily go farther left, but they can't occupy less.

That leaves 30 squares and you have a 27 block. So, if you count from the left, you see that the 27 block has to at least go to 27:11. If you count from the right, you see that the 27 has to go to at least 4:11, again remembering that we have to leave space for the 5 1 blocks. Hence, we've "bridged" this gap at all the squares from 4:11 to 27:11 *must* be marked. We don't know if it the 3 squares to either side are marked, but we can at least mark a bunch from this bridge.

As you practice, you'll see bridges quickly. For example, 3 empty squares can be bridged by a 2 block, 5 can be bridged by a 3 block, 7 can be bridged by a 4 block, and so on.

A great way to start is to find all the bridges you can, which usually means looking at the bigger numbers. For example, on a 40x40, you know that every number 21 or higher *has* to bridge, so find those straightaway. On a 30x30, you're looking at 16 or higher. These can provide a starting framework.

More importantly, as you're solving a puzzle, the null squares you identify will create smaller sections you can bridge. Effectively, the null square at 25:16 I talked about up above means the 10 block and the 13 block exactly bridge the left-hand part of that row.

You will bridge constantly. Again, see the power of the above example. Row 11 had a bridge and so did row 15 (1,1,1,1,17,1,4,1,1). Those provided the marked squares that permitted you to determine the null square at 25:16.

Let's look at the row 15 for a second for a small trick. That's a hard line to count. There are 9 different blocks and that's not easy. I use the right-click to temporarily mark a null square at the minimum spot for a block. So, for example, on this line, I'd go from the left and null mark columns 2, 4, 6, and 8 to match the beginning 1,1,1,1. Then from the right, I'd null mark columns 39,37,32, and 30. This allows me to see easily that the 17 easily bridges from column 9 to column 29 and I can mark the bridge from 13:15 and 25:15.

Then, and this is important given the power of null marks, I erase all the ones I just put down to help my eyes. Forgetting to erase leads to all sorts of frustration. Ask me how I know :)

Now, let's talk paperwork. Paperwork is marking which of the blocks you've identified using the power of the Puzzlemix site.

You know you left-click on a square to mark it and right-click to show it's null. You can also click on the blocks listed to the left and top *and* you can use both your light and dark colors. So, for me, I click a block as done with the dark color. Up above, I'd be able to not only place the 10 and 13 blocks on row 16, but I'd be able to click them as completed.

This is really important so you can make sure you know what's left on a row or column.

Also, I said you can use both colors. For me, I click the bridges I've made with the light color. So, up above, I'd highlight the 27 and 17 on rows 11 and 15 with the light color. That tells me that particular block has been started.

Sometimes, though, I need to count the number of blocks I've started to help me find null squares. I will use a light highlight of a block from either top or bottom (or left or right for rows) to mark that I've started a block. If I know which block it is, great, but I don't always. Still, knowing how many blocks you've started is often useful.

For example, let's assume you have a 40x40 column with the blocks of 3,1. That's a very small amount of marked squares meaning there's no way you'll be able to bridge it until much later in the solution. However, let's assume you are able to mark a block on this column by bridging row 10 and do the same on row 30.

So, this column has a marked square at row 10 and 30. The column requires a 3 block and 1 block, so only 2 blocks total. With those two marked squares, you've determined the two blocks and now you can null marks that can't be part of either block. In this case, that's easy. The bottom block is 1, so you have that one locked into place and you can click the dark color on the block number. The top block is 3, so you can't specify it exactly, but you know it will either go 2 above, 1 above-1 below, or 2 below, but that's it. This means you can mark or null every square on this column except those 2 above and below the marked square that's park of the 3 block.

Now all of the sudden, I've subdivided this puzzle, which may lead to new bridges, something I might not have noticed without doing the paperwork.

Paperwork is crucial for your eye. If you don't know where to click on the board, catch up on your paperwork. That will give you a bunch of clues or make everything clearer in your mind. Or both.

So, there you have the three most important tools.
1. Null squares to subdivide your puzzle
2. Bridging to provide marked squares
3. Paperwork

Do all three of those and you'll see Hanjies get much easier. Then you'll start doing them faster. I'm pretty quick at these, getting my share of top times so bring it on! I'll even give you an advantage. I don't count a puzzle as done until until I've clicked the dark color on every block and clicked the light color on every null square :)

Have fun!

Posted 22nd Jun 2026 at 01:56Thanks so much for posting the guide! I would however like to clarify that I don't roll my eyes, but instead feel slightly guilty for not having posted them yet. :)