The Illuminati just stole our office They shot JFK and have committed numerous crimes against humanity (not really) but we usually let that slide. But for stealing our offices, we have decided to get them arrested for those crimes, take over both offices, and get our revenge. In order to do this, though, we need their names.
To state the rules here:
- Congressmen are either Knights (R), Illuminati (L), Both (B), or Citizens (C)
- No one else belongs to either group
- We are not supposed to know who any member of either group is. So no more members of either group will willing reveal themselves.
- When attending joint meetings all of us are disguised but we can count how many of each of us there are
- After the plan is put into action, there will be no communication between us
- Citizens can't join either group by any means during this time frame. If you say their name and repeatedly tap your shoulders, they just start googling mental health centers to recommend to you.
- If a person (in this case always Bob) touches his left shoulder after saying a persons name, that person becomes an Illuminati (B) if he was only a Knight (R) or loses Illuminati (R) status if he was both (B).
- If a person (in this case always Bob) touches his right shoulder after saying a persons name, that person becomes a Knight (B) if he was only Illuminati(L) or loses Knight status (L) if he was both (B).
Senator Bob has been identified as a member of only our group and will not betray us. This is certain. We have agreed to hold a meeting every day with the Illuminati where every member of each group must be present in the correct uniform. If they are in both, they must wear the robes of one and the mask of the other. Bob will hold a prayer in front of congress between each meeting in which he can touch his shoulders as much as he likes and everyone will know.
We know there are only 100 congressmen whose status we don't already know. We know only 32 of these are in the Illuminati and 32 are our men. None of those unidentified are in both. Bob and Peter are currently known to be Knight Templar and Illuminati respectively because they shoulder tapped with obvious motives.
Is there a way we can determine the names of every one of those 32 congressmen who are right now Illuminati without revealing any of our names to them?
I am willing to lie and cheat as long as they don't know we are doing it. I am a politician like you after all.
Lets assume that we have ensure Peter will not shoulder tap again and they will not sabatoge us unless they know for a fact we have identified them (for now lets assume they are dumb enough they can't do that). They are smart enough, however, to try and catch us breaking meeting rules.
Bonus's if you can do any of the following:
- Minimize the number of meetings/shoulder tapping sessions
- Compute a plan for an arbitrary number of congressmen in each group
- Have the plan allowing for the possibility that unidentified congressmen is a member of both.