First, the good news: Nobody gets killed. 100 prisoners are out on parole, and the those who guess wrong will simply have their parole revoked. No blood. What a relief. The children will sleep well tonight.
But a lot of the usual stuff in the red hat / blue hat genre still applies:
- The Parole Officer (PO) will fit each parolee with a red hat or a blue hat.
- Each parolee can see all the other hat colors, but not his own.
- No communication is permitted. Just looking at hat colors.
Seriously, no shouting, pausing, singing, pointing, facial expressions.
If anything like that happens, then the PO will get PO'd and shoot everyone.
- On a common signal, each parolee will simultaneously guess the color of her own hat.
- Parolees initially meet, to formulate a strategy that dictates what color to guess, based on what she sees.
- The object is to guarantee the most successful guessers, regardless of the hat distribution.
And here's a wrinkle. There is a spy who informs the PO of the strategy.
So in placing the hats, the PO does his best to foil it.*
How many parolees can be saved?
* For example, if the strategy is to "guess the majority color" the PO will place 50 red and 50 blue hats, and no parolee will be saved.