problem link- http://www.spoj.com/problems/BADXOR/

i am not able to think of any solution other then brute force ,can anyone explain me how to proceed or can anyone give hint to the problem .also any suggestion on such type of problem or some links of similiar based problem will also be helpful

Problem link : http://www.spoj.com/problems/PYTRIP/

I am not able to think of any other solution except brute force and also, i am unable to find any pattern or something. If anyone could please give me a hint in approaching the problem or provide a reference to any material that you think might be helpful would be great.

link to the problem : https://www.hackerearth.com/practice/math/combinatorics/inclusion-exclusion/practice-problems/algorithm/gadget-fan/description/

I am only able to get 68 points when i submitted an O(n) solution. I am not able to optimize it further. I read the editorial as well but i wasn't able to understand it. So, if anyone could explain me the editorial or provide an alternate efficient approach to this problem.