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Red hat, blue hat
Posted 23 October 2013 - 05:04 AM
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.
Vidi vici veni.
Posted 23 October 2013 - 10:31 AM
Edited by harey, 23 October 2013 - 10:38 AM.
Posted 23 October 2013 - 11:06 AM
Standing in a certain position based on what you see is a form of communication.
Posted 24 October 2013 - 01:29 PM
Spoiler for 50 prisioners saved
Edited by ThunderCloud, 24 October 2013 - 01:34 PM.
Posted 24 October 2013 - 03:06 PM
edit: never mind
Edited by phil1882, 24 October 2013 - 03:09 PM.
Posted 24 October 2013 - 04:08 PM
Spoiler for Spoiler for 50
Actually, that conniving PO could foil this plan too, saving only 48...
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