What! terrorist?

Algebra Level 3

FBI, one of the most feared Law Enforcement Agency on this earth, has captured 100 terrorists. Out of these 100 terrorists, some ‘k’ are high valued targets and the agency plans to torture them.  It has marked all of the high valued targets with a sign on their head. Now the problem is, the person who has been tagged is not aware if he was actually tagged or not.  The inmates can see each other and the marks on the head of the tagged terrorists but they can’t communicate with each other. So, they have no way to determine if they themselves are tagged or not. All the “high valued” terrorists want an easy death instead of torture. They somehow manage a way to commit suicide, but then only the ones who are tagged will suicide. Also, they can commit suicide only during night.  Days pass by and nothing happens, but suddenly, on the night of 37th day, all the “high-valued” terrorists commit suicide. Determine, that out of the 100 terrorists, how many were the “high-valued” terrorists? 

Additional Info:  • k ≥ 1 i.e. atleast one “high-valued” terrorist exists! • Terrorists are aware that k ≥ 1, but they don’t know the value

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