A Puzzle With a Prize (6 ST Deadline)
Kwondre — Thu, 09/03/2009 - 13:52
Here is a logic puzzle/riddle. You will not already know the answer, because I just made it up myself. You can however get the answer very quickly if you turn off wow and think =).
First 3 correct responses get a "meaningful" prize in-game. It will be worth the while.
All correct responses after that get a "very very modest" prize in-game. It might not be worth the while.
Please send me all responses in private forum messages. DO NOT post the answer in this forum. DO NOT post clarification questions in the forum. Virtually everything you might need to know is in this post =).
Here is the puzzle / riddle:
- The odds of winning the lottery in New York State are 175,711,536 to 1
- Suppose you buy 175, 711, 535 tickets and all of them are losers.
- Suppose you then buy 1 single ticket for the same drawing.
- Did you win the lottery?
- Why? Why not?
The answer is very very specific, and if you get it you should think "Well Duh" like all good puzzles. "Because its probability" is not a suitable answer.
EDIT: Two hints and one clarification that I've given so far
1: Assume you are a logical being. Which means you're not going into this blind and you actually have a plan (i would hope so if you're buying 175 M + lottery tickets
2: Whether the jackpot is $350 M or $1, the odds of winning are still the same.
Clarification: The one leap of faith you need to make is that SOMEHOW you know that the first batch of lottery tickets you bought is a loser.
Here's why I win
Lunchbox — Mon, 09/07/2009 - 16:05Because if I had that type of money, I would not be buying lottery tickets in the first place.
LOL. Is this like your
Businessman — Mon, 09/07/2009 - 12:42LOL. Is this like your homework or something for school that you got to turn in?
Since I'm feeling a bit
Karli — Sat, 09/05/2009 - 11:52Since I'm feeling a bit cheeky I'll add this comment, which I already mentioned to Kwon, which is a nit-picky, but albeit important, clarification about odds vs. probability.
When you talk about odds and probability, they are both the chance in mathematical terms that you will win (or whatever you're defining). This is done by comparing the total number of favorable outcomes and the total number of ALL outcomes.
As an example, if you did a raffle that had 10 tickets, and there were three prizes, out of the ten tickets you would have 3 winners and 7 losers.
The PROBABILITY of winning this raffle is as follows: Total number of winners / (divided by) total number of all possible outcomes (3 winners and 7 losers = 10). Therefore, the probability of winning is 3/10, or .3 (30%).
The ODDS of winning this raffle are as follows: The total number of winners compared to the total number of losers. Therefore, the odds of winning are 3:7, or 1:2.3333. Odds are commonly expressed in terms of "one to x".
So, in the above mentioned example, if the ODDS of winning the lottery are 175,711,536 to 1, (ignoring the fact that there are general inconsistencies with the order of the winning chances/losing chances), that means that there are 175,711,536 losing outcomes and 1 winning outcomes. The total amount of POSSIBLE outcomes is those two numbers added together, or 175,711,537.
So...if you wanted to be REALLY nitpicky the answer to this riddle, using the same logic as the winning answers (which I believe I was one of the 4 to get right), is that there is a 50% chance of winning the lottery should you buy one more ticket, because if you wanted to truly guarantee a win you would buy not one but TWO more tickets to bring you to 100% of the total ticket pool outcomes.
The above answer was my first one =). I got the question "right" on my third try, after noticing that the term "out of", which implies probability and division, hence 1/175,711,536.
not enough information
Vitriola — Fri, 09/04/2009 - 11:47You did not say whether there were duplicates in the tickets purchased. They could have been randomly generated which would make this like the question of flipping a normal coin a million times, having it come up heads every time and what are the odds that it will be heads on the next toss.
If there are a total of 175,711,536 possible combinations, which information was not stipulated, and you purchased 175,711,535 with no duplicates, then the answer is simple. But this information is not given so how can we answer?
Mmmmm... You have to pay
Kwondre — Fri, 09/04/2009 - 12:20Mmmmm...
You have to pay money to buy a lottery ticket. So if you're paying 175 M+ to buy tickets, don't you think you would do your best to ensure you didn't buy two numbers combos twice?
And it is implicit that there are 175,711,536 possible combinations because i gave two pieces of information:
1) the odds of winning are 175,711,536 to 1 (which means there are 175,711,536 permutations).
2) I said whether the jackpot is $350 M or $1, the odds of winning are still the same (which should further cement that the odds are based on number combinations and not number of participants or anything variable like that).
I gave enough information in the question to answer it…but that doesn't mean you're exempt from using some deductive reasoning to get from question to answer.
Would this be a better riddle?
You enter a empty room with no windows and find a man hanging by his neck from a rope attached to the ceiling with a puddle of water on the floor.
Based on all information available in the above sentence what is the most likely cause of death?
(HINT: Water has three classical states of matter!!!)
The priest's leviatate buff
saedo — Fri, 09/04/2009 - 12:25The priest's leviatate buff ran out and some DK just outside turned on path of frost.
That's what lottery odds
saedo — Fri, 09/04/2009 - 12:13That's what lottery odds are. The number of possible cominations you can get.
Well I had to do a little looking too at their website to see how they do their lottery.
FYI, they do 5 numbers, from 1-56, same pool no repeating. Then throw in a 6th number, 1-46, different pool. And you have perfect freedom to choose any numbers you want.
So mathematically the odds are... A combinations formula with no repetition... Multiplied by the last number from the diff pool.
56! / ((56-5)! * 5! ) * 46 = 175,711,536 possible combinations. Which is what they gave the odds as.
And Kwondre was trying to give the hint of a "logical" being by implying you're not stupid and buy duplicates, you're buying every single combination there is out there.
Edit: More FYI... This is the fomula
where n is the number of things to choose from, and you choose r of them
(No repetition, order doesn't matter)
I think I can make the
Scaron — Fri, 09/04/2009 - 11:23I think I can make the argument that no truly reasonable person would ever find themselves that the person in the position in this thought was in. (Purchasing 175 million lottery tickets for the assurance of merely 350 million before taxes, requires a bit of a qwack).
If we assume that the person in question is a little loony, it also stands to reason that she or he is not a completely logical person. So while Kwon's math and logic is, I believe, flawless, the social science points me toward another answer.
If the person relies on some modicum of emotion when dealing with the numbers (and we almost always do see Tversky & Kahneman, 1974), we would be very surprised to see the person in question continue on down the path toward a lottery win.
This us illustrated by examining our probability of not winning the lottery. Most of us calculate this probability like this (and, implicitly at least, Kwon counted on this):
Let x = the number of possible lottery combinations.
P(not winning)= ((X- 1)!) / (X^X)
For those not mathematically inclined this works out to something greater than zero but not much greater than zero.
Now I would submit that the partly emotional gambler at least could, and at most probably would, see themselves as "unlucky" given that at some point should have won the lottery but to this point had not yet done so. Once they felt unlucky enough they would likely have given up.
What they didn't realize that Kwon did was that there was a key term missing from th probability of not winning above. In actuality that probability should be calculated thusly:
P(not winning lottery) = [((X- 1)!)(X-X)]/ [X^ X]
Looks complex but it's not. The true probability of not winning is zero. However, in my view, one key assumption was missing from the origional thought experiment: That the person buying the tickets was a Vulcan.
Edited: eqations for mathematical accuracy...logic remains the same.
How could you possibly know
PoTink — Fri, 09/04/2009 - 07:06How could you possibly know that the other tickets were losers unless the drawing had already happened???
I don't see how your question can be possible at all...ticket sales shut off at a set time before the drawing occurs and you can't possibly know all the other tickets you bought were losers unless you had seen the winning numbers.
And if you knew your other tickets were losers perhaps you're psychic or can time travel...but if you could do that, then why not just buy one ticket with the right numbers to begin with and save yourself the other $175,711,535?
So NO you're ticket is not a winner.
And even if you bought the ticket before the drawing occured and had covered all the possible # combinations, someone else may have purchased a winning ticket, so it would be a split jackpot.
look at the last line in my
Kwondre — Fri, 09/04/2009 - 07:29look at the last line in my post...i specifically said the one leap of faith you need to take is that you somehow knew that the original tickets were losers.
However, you don't even need to know that they're losers to answer the question.
I could have simply said "Will buying one more ticket guarantee you a win?" and the answer would have been yes - in the real world.
But phrasing the question like that would have been a much more boring question and frankly would give away the "trick" of the question...so I went with a leap of faith instead...you just didn't leap with me.
Split jackpots are possible; I never said anything about you being the ONLY person to win the lottery.
When it comes to money, I
PoTink — Fri, 09/04/2009 - 07:32When it comes to money, I typically err on the side of caution, so no, I didn't take that leap of faith with you. :(
Answer and a Related Bonus Question
Kwondre — Thu, 09/03/2009 - 19:04This answer is predicated on the following clairification note, which i edited into the original post: The one leap of faith you need to make is that SOMEHOW you know that the first batch of lottery tickets you bought is a loser.
175,711,536: This signifiies the number of possible lottery ticket combinations - which is why the odds are 1 in 175,711,536.
If you buy 175,711,535 tickets, that means you bought every possible combination of numbers except for ONE.
That means, assuming you came in with some kind of strategy, that buying that last combination would guarantee you would win the "jackpot" because you'd have one ticket for every combination.
Bonus question (Deadline, softly for tomorrow morning):
Last week the New York Mega Millions Jackpot was $350 M.
Knowing that the odds of winning are $175,711,536 to 1, and each ticket costs $1...why wouldn't you take out a loan for $175,711,536 to ensure that you almost double your money?
Modest prize for any and all correct answers. PST's please =)
Not exactly
Vitriola — Fri, 09/04/2009 - 11:53I know that in states that have a cash option, there is a lot less money in the mix. 400 million dollar prize value lotteries can be 270 million winners. This is because you can make a lot on the interest. Then, the IRS gets 28% under the "unearned income" bracket. NY gets a LOT on the income taxes as it has some of the highest tax rates in the nation, of course.
So, I would estimate that you would get half the face value at best. At worst, you would have to share that with anyone else that did the same thing. If it were not so, the banks would be doing that, or so it seems to me.
Goddamnit, Kwon, I posted
garreth — Fri, 09/04/2009 - 10:23Goddamnit, Kwon, I posted before this clarification. Now I feel like a bum.
Well, in with NY & Federal
Agoney — Fri, 09/04/2009 - 07:43Well, in with NY & Federal income taxes you'll be taxed to death so probably won't break even..
Your logic is off because of
Ewiges — Thu, 09/03/2009 - 19:13Your logic is off because of what I sent you. Also sending my answer for the bonus question which also says why your first answer is off.
your answer to the bonus
Kwondre — Thu, 09/03/2009 - 19:21your answer to the bonus question is correct...but your discussion of the first question is wrong.
The odds of winning the lottery in New York State...for the Mega Millions Jackpot...is exactly what i said it was in the first question....the odds are what they are PER ticket. that means you can "cover the board" and get every single possibility.
I never said anything about it being PROFITABLE...for example, if the jackpot is less than 175 M+, then its not worth it to cover the board....but the math still holds.
Wouldn't it be less than that
saedo — Thu, 09/03/2009 - 20:00Wouldn't it be less than that cause if even all the other tickets "lose" the jackpot, you get some cash if you get some of the numbers right. And with every possbility in your pot, there are lots of non-jackpot winning tickets too.
You still got it wrong. What
Ewiges — Fri, 09/04/2009 - 01:30You still got it wrong. What I'm trying to say is odds are not possibilities. The NY lotto has 941480149401 different possibilities. Odds just mean your chance of winning, its a ratio.
Now if every possibility were sold, one person per ticket, and no doubles, then the odds would equal the possibility.
Lottos basically come up with odds by calculating how many tickets will be sold, and how many winners there will be.
If the PTA plans on selling 1,000 raffle tickets, and they think there will be 2 winners... that would mean each ticket you buy is a 500:1 odd.
Odds in the sense of sports
Kwondre — Fri, 09/04/2009 - 04:52Odds in the sense of sports betting does not mean possibilities. The Colts can be 12 to 1 under dogs...doesn't mean there are 12 possibile outcomes.
But odds in a lottery? That DOES mean a FINITE number of possibilities.
Your PTA example...they "think" there will be two winners? That can only happen if they SELECT two tickets. If they select only ONE ticket...then the odds are 1 in 1000. A raffle is not on the same mechanics as the lottery.
I don't know where you're getting 941480149401, but you're either A) assuming the balls are repeating (which they aren't except for powerball, or B) not looking at the way Mega Millions work...but C) it doesn't matter for this example because I gave you the specific odds (or possibilities).
Yes it IS possible for multiple winners in the lottery...doesn't mean the ODDS or POSSIBILITIES per ticket change.
"Lottos basically come up with odds by calculating how many tickets will be sold, and how many winners there will be."
Wrong.
The odds are not based on how many participants. Go check the website again. Last week the jackpot was $350 M...this week the jackpot was something much much less (meaning less participants)....the odds are still the same. How is that possible, unless, OMG there are a set number of possibilities"
EDIT: I checked the math for u. Here it is (though like I said, you don't need it to solve the problem):
5/56 times 4/55 times 3/54 times 2/53 times 1/52 times 1/46 = 1 out of 175,711,536.
maybe
Vitriola — Fri, 09/04/2009 - 11:55"The Colts can be 12 to 1 under dogs...doesn't mean there are 12 possibile outcomes."
There could be if you count the spread.
Vitriola ... You can win, you
Shihli — Fri, 09/04/2009 - 12:01Vitriola ...
You can win, you can lose, you can tie.
Three outcomes at best. Not 12.
clarity of the words
Vitriola — Fri, 09/04/2009 - 12:07I was thinking that there could be more outcomes to the GAME as people can win by betting on the losing team. Win-lose-draw is so obvious that I did not think that you would need to specify it. As the alternative was not excluded by the words, that is what led me to think as I did.
/shrug
4 correct answers (two in the
Kwondre — Thu, 09/03/2009 - 15:274 correct answers (two in the same minute)
Big prizes gone...but small prizes left...small prizes are not bad...but maybe not that useful =)
3:07 Server Time...2 Correct
Kwondre — Thu, 09/03/2009 - 15:083:07 Server Time...2 Correct Answers...One more Big prize left....infinite small prizes left
2:42 Server Time. One correct
Kwondre — Thu, 09/03/2009 - 14:422:42 Server Time. One correct answer (second guess).
Are we going by mathematical
cromi — Thu, 09/03/2009 - 14:36Are we going by mathematical logic or philosophical logic?
I was a philosophy major in
Kwondre — Thu, 09/03/2009 - 14:41I was a philosophy major in College. There is no such thing as philiosophical logic that isn't based in some foundation of mathematics.
show me!
Vitriola — Fri, 09/04/2009 - 11:58"There is no such thing as philiosophical logic that isn't based in some foundation of mathematics."
Show me the math behind that statement. Remember that symbolic logic is not math as such even if it has some of the look and feel of it.
For me to do that, it would
Kwondre — Fri, 09/04/2009 - 12:45For me to do that, it would require me to give you an example of every single piece of philosophical logic that exists in the world and show the math behind it - and even then would not be sufficient because it would not cover pieces of philosophical logic that have not yet come into existence.
The burden of proof is on you, as all you need to do is come up with one example of philosophical logic that ISNT proven through mathematics and you win (unless I counter)
Are you sure symbolic logic isn't math?
Is "0=0" Math?
If so, why isn't "A <=>A" math?
I haven't done symbollic logic in years so i can't come up with a more sophisticated example.