Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

 Goliath wrote:
Let X = 0.999999999999...
Therefore 10X = 9.99999999999.....

Subtract X from both sides, so that:
10X - X = 9.99999999999.... - 0.99999999999.....
Which simplifies to:
9X = 9.00000000000....

Divide through by nine, so that:
X = 1
Therefore 1 = X = 0.99999999999.....
Proving that 0.99999999.... = 1

Nice effort... but I think I see the flaw. With 10X = 9.99999... you're assuming that 10x an infinitely recurring 9 is still infinitely recurring 9. However, multiplication is simply addition of lots, so the moment you begin with that first addition you're taking the recurring 9 over 1. This happens at all instances of the 9.
In other words - you're screwing up by trying to multiply infinity on something that isn't actually infinite and claiming that it'll be the same. There are certain circumstances where multiplying infinity will still result in infinity, BUT because we're talking about a number that is at a finite point (that is, it's 0.something) it's not truly infinite to begin with.

 Super Ready wrote:
[Nice effort... but I think I see the flaw. With 10X = 9.99999... you're assuming that 10x an infinitely recurring 9 is still infinitely recurring 9. However, multiplication is simply addition of lots, so the moment you begin with that first addition you're taking the recurring 9 over 1. This happens at all instances of the 9.
In other words - you're screwing up by trying to multiply infinity on something that isn't actually infinite and claiming that it'll be the same. There are certain circumstances where multiplying infinity will still result in infinity, BUT because we're talking about a number that is at a finite point (that is, it's 0.something) it's not truly infinite to begin with.

Just go with the other method then.

3 times 0.33333.... is 0.99999....

0.33333.... is 1/3.

3 times 1/3 is 1.

As such 0.99999..... is 1.

 sebster wrote:

 Super Ready wrote:
[Nice effort... but I think I see the flaw. With 10X = 9.99999... you're assuming that 10x an infinitely recurring 9 is still infinitely recurring 9. However, multiplication is simply addition of lots, so the moment you begin with that first addition you're taking the recurring 9 over 1. This happens at all instances of the 9.
In other words - you're screwing up by trying to multiply infinity on something that isn't actually infinite and claiming that it'll be the same. There are certain circumstances where multiplying infinity will still result in infinity, BUT because we're talking about a number that is at a finite point (that is, it's 0.something) it's not truly infinite to begin with.

Just go with the other method then.

3 times 0.33333.... is 0.99999....

0.33333.... is 1/3.

3 times 1/3 is 1.

As such 0.99999..... is 1.

So 1 is 25% of 3.99999?

 Super Ready wrote:

 Goliath wrote:
Let X = 0.999999999999...
Therefore 10X = 9.99999999999.....

Subtract X from both sides, so that:
10X - X = 9.99999999999.... - 0.99999999999.....
Which simplifies to:
9X = 9.00000000000....

Divide through by nine, so that:
X = 1
Therefore 1 = X = 0.99999999999.....
Proving that 0.99999999.... = 1

Nice effort... but I think I see the flaw. With 10X = 9.99999... you're assuming that 10x an infinitely recurring 9 is still infinitely recurring 9. However, multiplication is simply addition of lots, so the moment you begin with that first addition you're taking the recurring 9 over 1. This happens at all instances of the 9.
In other words - you're screwing up by trying to multiply infinity on something that isn't actually infinite and claiming that it'll be the same. There are certain circumstances where multiplying infinity will still result in infinity, BUT because we're talking about a number that is at a finite point (that is, it's 0.something) it's not truly infinite to begin with.

If it is a truly recurring decimal then it isn't a finite point. 0.99999999... Is meant to be an infinite number of nines after the decimal point, so multiplying it by ten would still mean an infinite number of nines, as you can't have infinitry minus one lots of something.

 d-usa wrote:
So 1 is 25% of 3.99999?

Yep, because 3.99999.... is the same thing as 4.

 motyak wrote:
The addition and multiplication ones were easy to see, I didn't expect them to go with the division thing though.

This one would work better vocally, haven't tried to write it down before (well to be honest I'm making it up as I go)

I have three eyes, two arms, two legs and two ears. What am I

A man.

I was going to go with 'me', but 'a man' is good enough.

The old 0.9999999 = 1 thing....


1 divided by 9 = 0.11111111....
2 divided by 9 = 0.22222222....
3 etc
4 etc
5 etc
6 etc
7 etc
8 divided by 9 = 0.8888888888....
Following the logic above
9 divided by 9 = 0.999999999..... Also known as 1

My favourites (even if they're dumb and for some reason mainly bear themed - from when I was a kid)

I'm in a house, all four windows face south. A bear walks past.
What colour is the bear?

This next one only works if you ask someone verbally.

You're driving a bus, 5 people get on, 3 get off, at the next stop 18 people get on and 6 disembark. At the next 37 people get on and 51 people get off the bus.
Whats the bus drivers name?

If a polar bear has a territory of 100 square miles and there are 10 penguins per square mile, how far has he got to go to eat 30 penguins?

PredaKhaine wrote:
You're driving a bus, 5 people get on, 3 get off, at the next stop 18 people get on and 6 disembark. At the next 37 people get on and 51 people get off the bus.
Whats the bus drivers name?

Even reading this, it stumped me until I went back through and was like, "wait where did it talk about the bus driver?"

While not explicitly riddles, I enjoy observation games, like Behind the Green Glass Doors, Magic Sticks, etc... those games where you have to watch the person doing it to figure out the trick to the game.

 Jasper wrote:

Following the logic above
9 divided by 9 = 0.999999999..... Also known as 1

Logic? No. 9 divided by 9 is 1. Not 0.99999999. It's 1.

1 is 25.0000625% of 3.99999.

You can round however you like, but it doesn't change the fact that 1 is not 25% of 3.99999. It's 25.0000625%. In nearly ever case, that 0.0000625% won't matter, though.

 d-usa wrote:

 Avatar 720 wrote:

 Alpharius wrote:
Does this thread need to be...

...baned?

Answer: This riddle is obviously working under an illusion of free choice, whereas we all know Dakka is a facist state where the opinions of its citizens means about as much to the malevolent supreme dictators in power as a penny does to the richest man in existence.

So it's like a Two-Party form of government?

Are you saying it should be? Are you deigning to tell our facist overlords how to police their own state? Do you want to be baned?

The 7:30am express train travelling at 60 miles an hour leaves Santa Fe bound for Phoenix, 520 miles away.
At the same time, the local train travelling 30 miles an hour and carrying 40 passengers leaves Phoenix bound for Santa Fe. It is eight cars long and always carries the same number of passengers in each car.
An hour later, a number of passengers equal to half the number of minutes past the hour get off, and three times as many plus six
get on.
At the second stop, half the passengers plus two get off, but twice as many get on as got on at the first stop.

Ticket, please.
I don't have a ticket.
Come with me, boy.
We've got a stowaway, sir.
I'll pay! How much?
Twice the fare from Tuscon to Flagstaff minus two thirds of the fare Albuquerque to El Paso!

riddle:

why do hot dogs come in packs of 8,

but hot dog buns come in packs of 12?


riddle:

when I drink grape juice and pee, where does the purple go?
(actually asked by a 5 year old when I was a camp councilour)

 easysauce wrote:
riddle:

why do hot dogs come in packs of 8,

but hot dog buns come in packs of 12?


riddle:

when I drink grape juice and pee, where does the purple go?
(actually asked by a 5 year old when I was a camp councilour)

ALL PURPLE GOES TO PURPLEFOOD!

 easysauce wrote:
riddle:

why do hot dogs come in packs of 8,

but hot dog buns come in packs of 12?

Because you are meant to buy 3 packs of hotdogs and 2 packs of buns. Thats 24 hotdogs.

Now 24 hotdogs means you got 12 people coming over for lunch, which means you need to buy beer.

A case of beer is 24 beers so now everyone can have a pair.

I thought hot dog buns came in packs of 10 and dogs in packs of 8. I can see if they came in packs of 6, 8, or 12, but 80 doesn't make sense until you reach 40 dogs...

Here's one:

 rubiksnoob wrote:
Here's one:

Spoiler:

Marvolous.

 sebster wrote:
Just go with the other method then.

3 times 0.33333.... is 0.99999....

0.33333.... is 1/3.

Here's where you went wrong. 1/3 =/ 0.3333... It is an approximation. 1/3 is essentially not representable as a decimal, but can be approximated by saying 0.333. Just like you can't multiple 3.14 by 2 and say that 2Pi is 6.28. That's an approximation.

 pretre wrote:

 sebster wrote:
Just go with the other method then.

3 times 0.33333.... is 0.99999....

0.33333.... is 1/3.

Here's where you went wrong. 1/3 =/ 0.3333... It is an approximation. 1/3 is essentially not representable as a decimal, but can be approximated by saying 0.333. Just like you can't multiple 3.14 by 2 and say that 2Pi is 6.28. That's an approximation.

Nonsense, that's what ... is for.

2Pi is 6.28..., but not 6.28. Pi is 3.14..., but not 3.14.

Wikipedia has a page for this.

EDIT:Grammar

Man, I love starting the 1=0.999... debates...

 whembly wrote:
Man, I love starting the 1=0.999... debates...

I think maths is an argument for a higher power, because only another being could come up with something so utterly sadistic.

 whembly wrote:
Man, I love starting the 1=0.999... debates...

I didn't even know this was a debated thing.

We went over it in my statistical analysis class. An already frayed mind was blown that day.

 xole wrote:

 whembly wrote:
Man, I love starting the 1=0.999... debates...

I didn't even know this was a debated thing.

Get two opposing mathematicians on this... and woah momma... EPIC geek-a-plosion!

So I can take 500 points of rares in a 1999 list?

 d-usa wrote:
So I can take 500 points of rares in a 1999 list?

A 1999 list? No. A 1999.99999 recurring list? Yes.

 Avatar 720 wrote:

 d-usa wrote:
So I can take 500 points of rares in a 1999 list?

A 1999 list? No. A 1999.99999 recurring list? Yes.

Shush, I'm trying to keep the non-stopping YMDC debate going!

I'm in a house, all four windows face south. A bear walks past.
What colour is the bear?

This next one only works if you ask someone verbally.

You're driving a bus, 5 people get on, 3 get off, at the next stop 18 people get on and 6 disembark. At the next 37 people get on and 51 people get off the bus.
Whats the bus drivers name?

If a polar bear has a territory of 100 square miles and there are 10 penguins per square mile, how far has he got to go to eat 30 penguins?