Best...Puzzle...Ever....

[Impeesa]

Here's a very tough one:

1000 prisoners are arranged in a big circle and chained to numbered posts from 1 to 1000 such that prisoner #1 is next to prisoner #1000. Their evil captor decides he will execute 999 of them. He begins by killing #1, then skips a prisoner and kills #3, then skips a prisoner and kills #5 and so on. When he's come full circle he continues by always skipping one surviving prisoner and killing the next one. In other words, corpses are removed and no longer count. Surviving prisoners are not moved: they remain chained to the post they started with. What will be the number of the one who survives in the end out of the 1000?

If anyone can solve this without using a computer or a physical model, I'll be very impressed.

I did it in my head*, then cranked off a computer simulation and got the same answer both times:

Spoiler

976

. Is that the answer you were looking for?

*I did make a few scribbled notes, but none of them involved writing out who was left and crossing them off. Basically just the upper and lower bounds of who was left after each iteration, which I also would have tracked in my head were I not so easily distracted. Hint to anyone still trying: At the point where you go from 125 left to 62 left, the rounding kicks in, shifts things over a bit, and #512 bites it pretty quickly IIRC.

--Impeesa--

 

[Revenge of the Bjorn]

OoH! ooh! I know a good one!

Okay outside of this town, there are two roads, one which leads to paradise, the other leads to Hell. Once you start down a road you cannot turn back. The roads are each watched by one of two identical twin brothers (who cannot be told apart by any means). One brother always tells the truth. The other always lies. You can ask one brother one question, and that's it. What one question can you ask to find out which road is which?

 

[Tuzenbach]

OoH! ooh! I know a good one!

Okay outside of this town, there are two roads, one which leads to paradise, the other leads to Hell. Once you start down a road you cannot turn back. The roads are each watched by one of two identical twin brothers (who cannot be told apart by any means). One brother always tells the truth. The other always lies. You can ask one brother one question, and that's it. What one question can you ask to find out which road is which?

You ask the one on the right which road *his brother would indicate* when asked which road leads to Paradise (assuming that's where you want to go). If it's the one that lies, then the direction indicated leads to Hell, as he's trying to deceive you. If it's the one who tells the truth, then the direction indicated must ALSO go to Hell, as the liar (in this case, the other one) would want you to go to Hell. So, you ask them the question and take the road *NOT* indicated, as this leads to Paradise.

I saw it on Doctor Who done with two robot mummies in "The Pyramids of Mars".

 

[MarauderX]

OoH! ooh! I know a good one!

Okay outside of this town, there are two roads, one which leads to paradise, the other leads to Hell. Once you start down a road you cannot turn back. The roads are each watched by one of two identical twin brothers (who cannot be told apart by any means). One brother always tells the truth. The other always lies. You can ask one brother one question, and that's it. What one question can you ask to find out which road is which?

Spoiler

hmmm... ask the one brother what the other brother would say is the way to hell, then go the other way. Yeah, that works, right?

 

[Tuzenbach]

I've five arms, six legs and a war face
Teeth inside, outside my head and a peace face
Thousands of eyes and ears and a justice face
A face for every occasion and another face



What am I?

 

[MerakSpielman]

One brother always tells the truth. The other always lies. You can ask one brother one question, and that's it. What one question can you ask to find out which road is which?

Spoiler

This was in Labrynth, too...

Easy if you know it. Kind of tough the first time you hear it.

 

[Zander]

I did it in my head*, then cranked off a computer simulation and got the same answer both times:

Spoiler

976

. Is that the answer you were looking for?

No, but you might be right nonetheless. This was 18 years ago so I may have recalled incorrectly, but I believe the answer is

Spoiler

978

. Can you run a computer model that goes through the process rather than use a formula?

 

[Tuzenbach]

Ooops! Did I kill the puzzle thread with my inclusion of a riddle?

;~D

 

[MerakSpielman]

No, we're all just trying to figure that bastard out. Can you give a hint?

 

[Impeesa]

No, but you might be right nonetheless. This was 18 years ago so I may have recalled incorrectly, but I believe the answer is

Spoiler

978

. Can you run a computer model that goes through the process rather than use a formula?

I didn't use a formula of any sort, when I did it mostly in my head I was just keeping track of a few important points, and my computer model did indeed run through the process manually to confirm my first answer. Yours is so very close to mine that it probably is just a case of clouded memory.

--Impeesa--