I never understood it when I was playing with physical toys when I was a child, but now that I have grown up, I understand it. In general, no matter how many times you multiply, just split it into 2×3 areas.

Let’s take 5×5 as an example (Figure 1):

Arrange the first three columns 1, 2, and 3 casually, then connect 4 and 5 together and place them in the area of ​​three rows and two columns in the upper right corner (Figure 2). Pay attention, 5 is in the front, 4 is in the back, and entering the upper two grids from the left is exactly the correct order.

Then arrange the three columns 6, 7, and 8 in the second row, and place 9 and 10 next to each other in the area of ​​three rows and two columns on the right (Figure 3). At this time, it is found that 10 is in the front and 9 is in the back, and when entering from the right, the reverse order will appear. So the two squares 10 and 9 were rotated half a turn along the two-by-two area (the results are shown in Figure 4). At this point, 9 and 10 can be arranged smoothly.

It can be summarized that the situation of positive order is: the large number is in the front and the small number is in the back, so you need to go in from the small side; conversely, if the small number is in front, you need to go in from the big side. The opposite of the forward order is the reverse order. In this case, the 3×2 area needs to be used to exchange the order of the two.

Now use the same method to arrange the third row (Figure 5). You can find that 14 and 15 are in reverse order. Fill them in after exchanging the order (Figure 6).

In the fourth row, since there is only one row left below, there is no way to form a 3×2 area on the right to exchange possible reverse order, so we arrange the two rows together from left to right.

The last two rows of the first column are 16 and 21. When they are placed in the area of ​​two rows and three columns, they are found to be in positive order, so they are placed directly (Figure 7). Put 17 and 22 in the same way (Picture 8). After adjusting 18 and 23 to the correct order and putting them in, the last three squares will definitely be able to be spelled (if the numbers are filled in in random order, there will be a 50% chance that the final result will be Can't spell three squares well).

Summary: Arrange row by row and column by row. The last two columns of each row borrow the next two rows and adjust the order. The last two rows borrow the right two columns from left to right and adjust the order. The last three cells must be in positive order.

PS As for speedrunning, it requires careful observation and some steps-saving tricks, and even sorting a larger area at the same time. I will not study it further here.