[Blofeld]

Nice problem. I hadn't met that one before.

I do know a neat relative of this problem. If anyone's interested, would people prefer I posted it here or started a new thread?

[joshs]

joshs, on Nov 20 2007, 04:58 PM, said:

Hannie, on Nov 20 2007, 04:18 PM, said:

bid_em_up, on Nov 20 2007, 03:23 PM, said:

Trumpace, on Nov 20 2007, 12:06 PM, said:

On a Sunday morning, every prisoner will be assigned a number (integer) from 1 to 100 (inclusive), which will be written on his forehead. Any number may be assigned to an arbitrary number of prisoners (repetitions allowed!)

Every prisoner will see the numbers of the other 99, but won't see his own number. The prisoners then guess their own numbers simultaneously. (There will be a guard assigned to each prisoner to note down the guess: yes, it is a high security prison)

If at least one prisoner guesses his number right, they are all released immediately. Otherwise, they will need to wait another year for another challenge.

On the evening before, they are allowed to gather together and devise a strategy.

What should the prisoners' strategy be?

Certainly, the odds are better if they either:

All say the same number (100 chances of getting 1 number right) or,

Split up into groups of 2, 5, 10, 20, 25 (pick one) and each group guesses a different number that they can see.

Are they not?

No. It's not such an easy problem. If you have no idea how to attack the problem then I'd recommend looking at my hints and trying to solve it for 3 prisoners. Guessing the solution is unlikely to work.

But you wrote your hints in invisible ink....

Anyway, here is my algorithm for N people:

Spoiler

First I renumber everything by subtracting 1 from every number.
We also number the people from i= 0 to N-1.
Then we note that Mod N the sum of all the balls =0,1,2,...,N-1

So I propose an algorithm such that if the SUM Mod N=k then the k'th person will be correct:

Person 0 Forms {- Sum (of the other numbers) } Mod N . This is his guess.

Person 1 Forms {1 - Sum (of the other numbers ) } Mod N. This is his guess.

And so on. Person i forms
{i- Sum (of the other numbers) } Mod N. This is his guess.

[finnigan1]

A rather simple one, get close enough to see an other inmate's eyes clearly.
no need to ask or communicate, but look carefuly and you will see your own number reflected [in reverse] in the other inmate's eyes.
Next question ....

[Trumpace]

Well done guys (you know who you are).

Blofeld, please create a new thread for the problem you had in mind.

finnigan1, please re-read the thread No "silly" solutions.

bid_em_up, criminals can be smart/know math (unabomber?)... why not? (and just because they got caught does not mean they are stupid)

[bid_em_up]

double post

[bid_em_up]

Trumpace, on Nov 20 2007, 06:52 PM, said:

bid_em_up, criminals can be smart/know math (unabomber?)... why not? (and just because they got caught does not mean they are stupid)

Ever been in a jail? Or know anyone who has? Ask them sometime about the intelligence level in prisons.

While you may have one or two (or even 4/5/6) who might be smart, you would not find 100 of them capable of performing this calculation all in the same prison, all at the same time.

Heck, I have 5 quarters of college level calculus in my background (albeit some 25 years ago) and I am not even sure I could do it.

[Trumpace]

bid_em_up, on Nov 20 2007, 07:27 PM, said:

Trumpace, on Nov 20 2007, 06:52 PM, said:

bid_em_up, criminals can be smart/know math (unabomber?)... why not? (and just because they got caught does not mean they are stupid)

Ever been in a jail? Or know anyone who has?

While you may have one or two (or even 4/5/6) who might be smart, you would not find 100 of them capable of performing this calculation all in the same prison, all at the same time.

Hell, I have 5 quarters of calculus in my background (albeit some 25 years ago) and I am not even sure I could do it.

Eh? I was just kidding (and was under the impression that you were too based on your smiley)... Apparently, you were being serious.

Practically speaking, do you really think there will be such a warden? OR a prison with exactly 100 inmates and 100 guards? OR that the warden will be allowed to release them in such a way? OR that the prisoners will agree to have a number written on their foreheads? OR we will know about such events?

Please... lets not discuss this any futher.

[bid_em_up]

Trumpace, on Nov 20 2007, 07:40 PM, said:

Eh? I was just kidding (and was under the impression that you were too based on your smiley)... Apparently, you were being serious.


Please... lets not discuss this any futher.

I was kidding. I thought you were being serious (no smiley after your statement).



Ok

[Trumpace]

bid_em_up, on Nov 20 2007, 08:56 PM, said:

Trumpace, on Nov 20 2007, 07:40 PM, said:

Eh? I was just kidding (and was under the impression that you were too based on your smiley)... Apparently, you were being serious.


Please... lets not discuss this any futher.

I was kidding. I thought you were being serious (no smiley after your statement).



Ok

ok

[barmar]

Maybe it's one of those low-security prisons whether they send only white-collar criminals. Lots of stock brokers who committed fraud, Enron-types, con men, etc. These people could handle the math, I think.