Another Logic Problem

fnord_too · #1 05-17-2005, 02:52 PM

I don't know if this is one that has been arround or not...

There is a completely isolated village where everyone sees everyone else every day. One day, a superior being (SB) comes to the village and offers to be their benefactor provided all the sinners leave. The villagers are agreeable, but they do not know who the sinners are (even the sinners themselves don't know they are sinners). The being places a mark on all the sinners foreheads in such a way as those marked have no idea they have been marked. There are no reflective surfaces in the village. No one will tell another villager they are marked. Once a villager knows he or she is marked, they will leave the following morning. Label the day the SB made the arrangement as day 0, and everyone saw each other on day zero after the arrangement was made.

On day five all the sinners (and only the sinners) left the village. How many sinners were there?

Rasputin · #2 05-17-2005, 03:04 PM

Four.

Everyone sees four marks and doesn't see their own so everyone knows there are either four sinners or five sinners and if they can determine that it is five they will know they are one as well.

If there were one sinner, there would 99 people who saw one and 1 person who saw none so the guy who saw none would know he was one and leave on Day 1.

If there were two, they would both see one other sinner and expect him to leave on Day 1. When he doesn't, they both realize that there are two sinners and since they can only see one, they know that they are the other one and leave on Day 2.

If there are three, they expect folks to leave on Day 2 but when they don't, they know there are three, and they're one and leave on Day 4.

Once Day 4 passes you know there are five. If you only see four, you know you're one and you leave the next morning.

So if all the sinners leave on Day 5, there are four of them.

fnord_too · #3 05-17-2005, 03:27 PM

[ QUOTE ]
If there are three, they expect folks to leave on Day 2 but when they don't, they know there are three, and they're one and leave on Day 4.

Once Day 4 passes you know there are five. If you only see four, you know you're one and you leave the next morning.

So if all the sinners leave on Day 5, there are four of them.

[/ QUOTE ]

I think you skipped a day in there (in the bolded part). Your reasoning is correct, without skipping the day you get to 5.

Rasputin · #4 05-17-2005, 04:18 PM

Yeah, I skipped a day because it would have been just like the other days and I figured I'd made the point.

There was something similar around here about six months or so ago.