If we take all the digits from 1 to 9 and lay them out in order.
Now repeat the sequence and add it to the end.
Now let's copy and reverse everything to create a second sequence
Now we merge both together and wrap them into a circle. So we have 18 digits running in order clockwise and 18 digits running in reverse anticlockwise.
The above image is an example of how the numbers could be arranged
Now if we examine the arrangement we can find a place where we can split the circle into orthogonally connected sections of 9 cells where no digit repeats.
Is there are way of arranging the gaps between the clockwise and anticlockwise sequences around the circle in such a way to make it impossible to divide the circle into 4 sections where each section contains all of the digits 1 to 9 without repeats?
Or can you prove that no matter how the 2 sequences interweave around the circle there will always be a place where you can split the circle into 4 groups without repeated digits?
The star in the image is meaningless