1. for the numbers you have given :

500 = 111110100 (in binary form)

now let 9 prisoners come out and drink

now take your prisoner’s 1 through 9 and let prisoner 1 take a sip from every bottle that has a 1 in its least significant bit. let prisoner 9 take a sip from every bottle with a 1 in its most significant bit. etc.

prisoner 9 8 7 6 5 4 3 2 1
bottle 500 1 1 1 1 1 0 1 0 0

Depending on which all prisoners died, allot those bits as 1 and those who lived as 0

Then form the corresponding binary number of 9 digits and get the decimal conversion and u have your bottle number

2. That's it.

Follow up question (I always make follow ups): How many slaves the king has to risk if there are not one, but two poisoned bottles?

3. Originally Posted by 8ankitj
Using some tedious math, I figured that all paths are equally likely (there might be an easier way to show that too).

Here's another followup question worth trying: What is the probability that you will pass through the point whose coordinates are (i, j)?

Is anyone interested or am I talking to myself?
This was kind of straight forward. This should be the answer:

$\frac{\left (^{i+j}{C}_{i}\right)\left (^{m-i+n-j}{C}_{m-i}\right)\left}{^{m+n}C_{m}}$

4. Originally Posted by 8ankitj
That's it.

Follow up question (I always make follow ups): How many slaves the king has to risk if there are not one, but two poisoned bottles?
If you got the answer as 17, that is wrong. I got that too, but then when I started working out the "how" part, I realized it doesn't work. This is turning out to be very challenging. Haven't solved it yet...

5. anyone wanna teach me how to do laplace transformations?

6. Originally Posted by Riggins
anyone wanna teach me how to do laplace transformations?
Can teach you lapdance protocol instead.

7. demo's from your chiK and we have a deal.

8. Originally Posted by Riggins
anyone wanna teach me how to do laplace transformations?

www.stanford.edu/~boyd/ee102/laplace.pdf

9. Originally Posted by Riggins
anyone wanna teach me how to do laplace transformations?
Linear functionals that make solving some differential equations really quite easy, because they turn a differential operator into an algebraic one. There are tables of them all over the internet. Not much more to say, really.

There is some theory behind them which leads to some interesting stuff, but assuming you aren't doing complex analysis or PDE theory, you don't care about those. Just look up tables.

===

Three algebraic topology assignments down. Starting to really enjoy this ****.

10. Originally Posted by Spark
Linear functionals that make solving some differential equations really quite easy, because they turn a differential operator into an algebraic one. There are tables of them all over the internet. Not much more to say, really.

There is some theory behind them which leads to some interesting stuff, but assuming you aren't doing complex analysis or PDE theory, you don't care about those. Just look up tables.

===

Three algebraic topology assignments down. Starting to really enjoy this ****.

11. Originally Posted by 8ankitj
If you got the answer as 17, that is wrong. I got that too, but then when I started working out the "how" part, I realized it doesn't work. This is turning out to be very challenging. Haven't solved it yet...
yes this looks pretty tough unless you are said the relative positions of both the bottles

12. What do you mean by relative position?

It will be straightforward if the two poisons only worked when consumed together and not when taken without one another. In that case every possible set of fatalities should point to a unique combination of the 2 bottles that were BOTH tasted by everyone in that set. So 2^n should be greater than 500C2. That gives 17 as the answer.

But if the poisons can work on their own, then every possible set of fatalities should point to a unique combination of 2 bottles, AT LEAST ONE of which were tasted by everyone in that set.

Going from BOTH to AT LEAST ONE is proving to be very hard. I'm hoping that this problem will translate to something else I've come across before but to no avail so far.

13. Possible Breakthrough in Math's ABC Conjecture

Light reading for when the cricket gets boring.

Edit: "Intrinsic Hodge Theory"

14. An article with links to the papers if your life just ain't complicated enough.

Seriously, this stuff is all kinds of ****ed-up. I glanced briefly at all 4 of the papers and was sure of my ground when I saw the word 'the', started to get a little more nervous at mentions of 'I', thereafter;

/technicaldiscussion

15. I spent a minute trying to work out how 16 is divisible by 42. Eventually realised it was a transcription error.

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