The circuit as is explained is formed of the motion from the number 2-3-5-9-8-6-2 etc. What can be noted about the circuit is that it is formed of an increasing number. 2-3 is 1, 3-5 is 2, 5-9 is 4, 9-8? Well this riddle is solved by cross addition for of course if we look at the pattern we can see that it has been doubling each time. Thus if 5-9 is four then 9-8 must be the double of this i.e. 8. So 9+8=17 and (17)+= 8. Of course we could know that because 9=0. Does this subsequently work? Yes of course it does.
8-6 is our next objective which must be achieved by the doubling of 8 (16), so 8+16=24 and (24)+=6. 6+32=38 and (38)+=(11)+=2. We are back to the start. Here we have a new circuit. 1-2-4-8-7-5-1 which makes a similar shape on a grid like