Puzzle Quiz #2
- Thread starter Syterion
- Start date
AVN
Deity
No, I will correct it.Yom said:
Actually, that may not be it...AVN
Deity
Fetus4188 said:
It's correct
Just to be sure that you haven't guessed can you tell on which number he lives, what the color of his house is and which beverage he drinks ?
Fetus4188
Deity
- Joined
- Apr 16, 2004
- Messages
- 3,629
Uhhg, I just threw out the paper I did it on, it involves using the few knowns to find the unknowns by using the clues given. I started by knowing that the Norwegian was in the first house, the one to his right is blue, and the one in the middle is a milk-drinker, from there I deduced the rest by using the clues/finding out what things are not possible for which house, etc., I would tell you more but I don't feel like doing it over, or digging through the garbage.
Timko
King
Can't...let...thread.......die.
Ok here's one.
You go to a casino and they have a new game.
You pay x cents per play and the dealer puts down 1c on your side.
He then flips a coin.
If it's tails then you take what is on your side and the game is over.
If it's heads the dealer then doubles what you have to 2c and flips again.
etc.
So if its HHHT you get 8c back.
Unfortunately the x cents per play is quite high. How high would it have to be before you would no longer want to play. Assume you have plenty of capital.
Ok here's one.
You go to a casino and they have a new game.
You pay x cents per play and the dealer puts down 1c on your side.
He then flips a coin.
If it's tails then you take what is on your side and the game is over.
If it's heads the dealer then doubles what you have to 2c and flips again.
etc.
So if its HHHT you get 8c back.
Unfortunately the x cents per play is quite high. How high would it have to be before you would no longer want to play. Assume you have plenty of capital.
Perfection
The Great Head.
Any finite amount would be acceptable
Mathilda
Queen
I must be hard of thinking these days, I don't again understand the question.
So I'll ask: Do I loose the money I payed to play in the first place whatever happens?
Either way, if I assume that I have plenty of capital, I don't expect I could be bothered to sit there watching cents being shifted and coins flipped. there doesn't seem to be very good chances of winning any significant amount of money in this.
And no, I don't do the lottery either.
Ok, I actually looked at the way the winnings increase and the way propabilitites decline, and taking into account the boredom factor answer is this:
I'd play three rounds if the x wasn't more than 50c.
Quite sure you was after something far more mathematical, but buggered if i know what it was
So I'll ask: Do I loose the money I payed to play in the first place whatever happens?
Either way, if I assume that I have plenty of capital, I don't expect I could be bothered to sit there watching cents being shifted and coins flipped. there doesn't seem to be very good chances of winning any significant amount of money in this.
And no, I don't do the lottery either.
Ok, I actually looked at the way the winnings increase and the way propabilitites decline, and taking into account the boredom factor answer is this:
I'd play three rounds if the x wasn't more than 50c.
Quite sure you was after something far more mathematical, but buggered if i know what it was
Perfection said:
Because every time your chance of winning halves, the payout doubles.
Payout/Probability of payout
1 * 1/2
2 * 1/4
4 * 1/8
8 * 1/16
16 * 1/32
32 * 1/64
64 * 1/128
128 * 1/256
As can be seen, in every case the odds are 1/2. So, no matter how much you pay to play, there is some higher value of payout that gives even odds of compensation. And since you're given the first cent as a freebie, the game is permanently weighted in your favour by (an admittedly negligible) amount.
Of course, it would be really stupid to play this game at all, in my opinion.
Scuffer
Scuffer says...
So you win a cent a go on average.
In which case, the maximum amount to stake would be a ratio to amount of capital to have, dependant on how much risk you like to take.
I prefer the horses.
In which case, the maximum amount to stake would be a ratio to amount of capital to have, dependant on how much risk you like to take.
I prefer the horses.
Timko
King
Perfection wins.Perfection said:
The point is that even if they charge $500,000 per turn it is still theoretically worth it because the expected value of winnings per turn is infinite. Since
E[payout] = sum{payout*P(payout)}
=1 * 1/2
+2 * 1/4
+4 * 1/8
+8 * 1/16
+16* 1/32
+32* 1/64
which is an infinite series.
Having said that you need 26 heads in a row to get over $500,000 and the likelihood of getting back less than $500,000 every turn is 97% if you have a trillion dollars in capital.
I don't think I would play the game.
Perfection
The Great Head.
That probobility seems very hard to get, how did you do it?Timko said:
New series
20509, 140523, 230119, 100111, 21801
What's next
Timko
King
Well I did 2^{-26} to get the chance that you get $500,000 in one turn.Perfection said:
1-2^{-26} to get the likelihood that you don't get $500,000 in one turn.
(1-2^{-26})^{2,000,000} to get the likelihood that you don't get $500,000 every turn for the 2 millions turns you have with a trillion dollars in capital.
Perfection
The Great Head.
But that doesn't count all the money you make in the process.Timko said:
Hey, it's logical (and not too difficult, might I add)Yom said:
Syterion
Voodoo Economist
If noone will solve Perf's than I'll post one.
I think it is pretty easy, but oh well.
Here is a numbered list of statements, some true, some false, which refer to a specific number (unique positive integer, base 10).
It just so happens that if a statement is true then its index number appears among the number's digits, and if a statement is false then its index number does not appear among the number's digits.
0. The sum of the number's digits is a prime.
1. The product of the number's digits is odd.
2. Each of the number's digits is less than the next digit (if there is one).
3. No two of the number's digits are equal.
4. None of the number's digits is greater than 4.
5. The number has fewer than 6 digits.
6. The product of the number's digits is not divisible by 6.
7. The number is even.
8. No two of the number's digits differ by 1.
9. At least one of the number's digits is equal to the sum of two other digits. (Any of the digits may be equal, as long as all 3 digits are distinct... for example: {2, 2, 4} or {2, 3, 5} )
What's the numbah?
I think it is pretty easy, but oh well.
Here is a numbered list of statements, some true, some false, which refer to a specific number (unique positive integer, base 10).
It just so happens that if a statement is true then its index number appears among the number's digits, and if a statement is false then its index number does not appear among the number's digits.
0. The sum of the number's digits is a prime.
1. The product of the number's digits is odd.
2. Each of the number's digits is less than the next digit (if there is one).
3. No two of the number's digits are equal.
4. None of the number's digits is greater than 4.
5. The number has fewer than 6 digits.
6. The product of the number's digits is not divisible by 6.
7. The number is even.
8. No two of the number's digits differ by 1.
9. At least one of the number's digits is equal to the sum of two other digits. (Any of the digits may be equal, as long as all 3 digits are distinct... for example: {2, 2, 4} or {2, 3, 5} )
What's the numbah?
Perfection
The Great Head.
Conditions 7 and 1 are mutually exclusive.
