100 Married Couples
If every husband cheats and every wife knows when another woman's husband cheats, then every wife is already aware of cheating in the village. The queen has introduced no new data.Furthermore, if each wife is aware of 99 instances of cheating and we assume she isn't stupid, she can probably surmise through induction that all 100 husbands have cheated. If word gets out, it will be a bloodbath. The entire community will be destroyed. The only solution is to never, ever seek out any information that would prove that her own husband is unfaithful. If everyone keeps quiet, the burden of proof rests with the queen alone.
Essentially, it's a classic "garbage in, garbage out" problem. The wives subvert the data-collection process, and the algorithm fails for lack of input validation.
12 coin problem
than is should and, and this is the real kicker, your weighs must be non-adaptive. that is, your choice of what to put on the balance for your second weigh cannot depend on the outcome of the first weigh and your decision about what to weigh for round 3 cannot depend on what happened on either your first or second weigh. for example, you can't say something like "take coin #1 and coin #2 and weigh them. if they balance, then take coins 3,4,5 and weight them against 6,7,8...if 1 and 2 don't balance, then weigh #1 vs #12..." you
have to say something like:
round #1: do this
round #2: do this
round #3: do this
if the results are left tilt, balanced, and left tilt, respectively, then coin #11 is heavier than it should be.
Answer it is here.