October 2020
[url]https://www.research.ibm.com/haifa/ponderthis/challenges/October2020.html[/url]
This one looks complicated 
The control graph example image at the end ("Here's a sample program, along with its controlflow graph:") doesn't seem to load.

The question is also illposed, needs many clarifications. For example: how does the algorithm will work for negative integers? Return value of modulo operation changes from one programming language to another.

Here are the different results of modulo operation for negative numbers in some commonly known languages:
[URL="https://torstencurdt.com/tech/posts/moduloofnegativenumbers/"]https://torstencurdt.com/tech/posts/moduloofnegativenumbers/[/URL] 
Possible hint if I understand the question correctly (I agree that the language is not very clear).
[SPOILER] Hint: https://cs.stackexchange.com/questions/63572/whatisthemathcaloofsubtractionbasedgcdalgorithm [/SPOILER] 
Can anyone explain to me
 why the ** in "**20** lines"?  why the $ in "length $n$"?  which other path than 102030407090 is possible in the sample program?  what will say "the number of paths ... is the sequence 0,2,2,...?" Isn't the number dependent of a,b? Does 0 make sense? Perhaps I'm the only one who doesn't understand this. 
[QUOTE=Dieter;558925]Can anyone explain to me
 why the ** in "**20** lines"?  why the $ in "length $n$"?  which other path than 102030407090 is possible in the sample program?  what will say "the number of paths ... is the sequence 0,2,2,...?" Isn't the number dependent of a,b? Does 0 make sense? Perhaps I'm the only one who doesn't understand this.[/QUOTE] Trust me, you are not the only one. I think ** and $ is just for formatting, and you can ignore. The sample program is not an indicator of what to expect from the real problem, let alone the missing image is not helping at all. 
Its similar to assembly codes :smile:
[SPOILER]I think its about how to make jump below( jump condition on a>b or a<b) logic within 20lines[/SPOILER] btw I still dont know why they added chaos operator 
It's no problem to write a code with 20 lines (not using "chaos lines", of course) for the search of the gcd, if I take a>b>0 for granted, and to draw the controlflow graph. But the paths are dependent of a and b, and so I don't know how to achieve the given sequence. And the zero!

I interpreted it as creating the controlflow graph based only on the existence of jump commands, so it does not depend on values of a and b. Actual behavior of the program will depend on those, but the graph won't.
I believe the sequence 0, 2, 2, ... starts from 1 for path length (that's another kindofflaw in the problem description, as it links to an OEIS sequence with a definition that doesn't match, without mentioning that you need a different offset). The 0 means that there is no direct path from the starting node in the graph to the end node, then 2 means there are 2 possible paths with 2 steps. 
[QUOTE=uau;558979]I interpreted it as creating the controlflow graph based only on the existence of jump commands, so it does not depend on values of a and b. Actual behavior of the program will depend on those, but the graph won't.
I believe the sequence 0, 2, 2, ... starts from 1 for path length (that's another kindofflaw in the problem description, as it links to an OEIS sequence with a definition that doesn't match, without mentioning that you need a different offset). The 0 means that there is no direct path from the starting node in the graph to the end node, then 2 means there are 2 possible paths with 2 steps.[/QUOTE] Thank you. Good explanation. The length of a path from the entry node to the exit node is the number of needed edges. a6 = 17 will say that there are 17 different paths from entry to exit needing 6 edges. Meanwhile the cfg of the example can be seen, and it were a good exercise to write down the sequence: 0,0,0,1,... (there is no path of length 1,2,3 and only one path of length 4) Unfortunately I don't understand the edge from 60 to 70. 
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