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you can easily divide a cake between 3 people.

just cut it into thirds.

but you cannot divide a cake between 3 people

by cutting pieces that are 33% percent of the whole

because someone will wind up getting 34%

and you can't do 33.3333333%

cuz someone will still get more than the others

so if you can divide it into thirds, then why can't you divide into three pieces with percents?

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Posted · Report post

but you cannot divide a cake between 3 people

You're aware that you're giving false information in your riddle, right?

by cutting pieces that are 33% percent of the whole

because someone will wind up getting 34%

and you can't do 33.3333333%

cuz someone will still get more than the others

Each person gets 33.333...%

so if you can divide it into thirds, then why can't you divide into three pieces with percents?

You can.

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so if you can divide it into thirds, then why can't you divide into three pieces with percents?

Because we use base 10 numbering. (Of course, all numbering systems would be called base 10 in their own base...but you know what I mean.) If we used base 3 numbering, then 100 would represent the decimal number 9, and a third would be represented by the number 10%. (Note that one-half, or what in decimal we call 50%, would not be representable by a terminating "decimal" expansion in base 3 percent representation. It would be 11.1111111111...%)

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In other words, you could cut it using percents, however, you wouldn't due to the fact that fractions are more precise than percents.

33.33333333333333333333333333333333333333333333333333333333333333333333333333333

333333333333333333333333333333333333333333333333333333333333.....% would still technically be 1/3 it just never ends, so you can't see the fact that it is 1/3.

If you were to go to the end of the infinite decimal, you would find that it is.

however, this is all beside the point, because if I had a cake I would simply eat it all and not share!!!!

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fractions are more precise than percents.

No, they're not.

1/4 = .25

1/3 = .333...

Remember, the = sign is never used loosely in mathematics. 1/3 is exactly equal to .333...

And yes, .999... is equal to 1.

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fractions are more precise than percents.

Well, all rational numbers do have exact representations as integer ratios; but not as finite-length decimals.

But irrational numbers [pi, e.g.] lack exact representations both ways.

pi ~= 22/7

pi ~= 3.1415926536 ...

Now, although the precision of both representations can be improved to an arbitrary level,

it's much easier to add a digit to the decimal representation than it is to find the next-more-precise integer ratio.

Also, just as 1/3 may look more compact than 0.333333 ...

one can say .3 looks more compact than 1/0.33333 ...

But to be fair .3 and 3/10 are about the same.

Your comment is interesting but not generally true.

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Posted · Report post

thank you I guess

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Ya know what I love about you, Ploper? It always seems you genuinely appreciate being shown that something has a different answer than what you expected without letting your ego get in the way. I think most of us would be better off if we could do that. Now if we could only convince you that if a parent has two kids and at least one of them is a girl, the probability that the other kid is also a girl is 1/3. ;)

Anyway, glad you're here and I hope you'll be sticking around for a long time to come.

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speaking of numbers, did you know that the average person has less than one leg?

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thanks Martini

but that doesn't stop me from being stubborn.

I don't understand how .999 could = 1

becuase if you look at what isn't there, the .001

that .001 is something

if .999=1 then .001 must equal 0

but something, no matter how small, is more than nothing.

unless they all have 33.333333% and throw away 0.000001% (which, granted, is next to nothing)

the equal value cannot be expressed as a decimal.

I know someone will correct me and we'll all be on our way.

I learn from saying stupid things then havin people on here correct me

it's the reason why people I know think I'm smart

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I don't understand how .999 could = 1

becuase if you look at what isn't there, the .001

that .001 is something

if .999=1 then .001 must equal 0

.999 doesn't = 1

but

.999... does = 1

.333... = 1/3

.333... + .333... + .333... = .999...

1/3 + 1/3 + 1/3 = 1

.999... = 1

Consider the following riddle (ignore the laws of physics):

There is a being with supernatural powers that can move very, very quickly. He flicks the switch to a lamp to the on position. He waits exactly 1 minute and turns it off. He flicks it back on after 30 seconds. He flicks it off after 15 seconds. He flicks it on after 7 1/2 seconds. He continues in this manner (flicking the switch after waiting exactly one-half the time he waited before hitting it the last time). How long before he's finished?

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thanks again martini

now I finally understand what's goin on.

plus, I'm finally convinced with the 1/3 thing, based on a conversation with my friend.

YAY

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Just wanted to bring up the fact that trying to divide a cake by percentages is inherently dangerous and destructive.

At some point. in your quest to achieve an exact 33.33333333333333333333333333333333333333...% division of the cake, two out of three cakes will force you have a left over atom or two.

WARNING: Do NOT try this at home:

Splitting one of those left over atoms will solve your problem - in fact, it will solve ALL your problems... and your neighbours... and most of your hometown...

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Just wanted to bring up the fact that trying to divide a cake by percentages is inherently dangerous and destructive.

At some point. in your quest to achieve an exact 33.33333333333333333333333333333333333333...% division of the cake, two out of three cakes will force you have a left over atom or two.

It's not because you're dividing it by "percentages" though; it's just because you're dividing it. You divide it equally whether or not you say each person gets one third or each person gets 33.333...%.

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two out of three cakes will force you have a left over atom or two.
If they're chocolate atoms, [shhh!] I will remove the problem by volunteering to eat them.
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Posted · Report post

its very simply divided:

all 3 people do rock/paper/scissors and the loser cuts, the winner picks a piece first, and the second place winner gets the second choice.

the loser/cutter gets the remaining piece.

how much more fair than that can you get?

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Posted · Report post

its very simply divided:

all 3 people do rock/paper/scissors and the loser cuts, the winner picks a piece first, and the second place winner gets the second choice.

the loser/cutter gets the remaining piece.

how much more fair than that can you get?

What outcome of RPS gives you a winner, a 2nd place winner and a loser?

RRR, PPP, SSS and RPS are useless.

RRP, PPS and SSR gives two losers

RPP, PSS and SRR gives two winners.

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What outcome of RPS gives you a winner, a 2nd place winner and a loser?

RRR, PPP, SSS and RPS are useless.

RRP, PPS and SSR gives two losers

RPP, PSS and SRR gives two winners.

"Good ol' rock! Nothing beats rock."

-- Bart Simpson

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each person plays the other two people.

if there's a clear cut winner (ie, one person won against both other players), then the two losers play for second place.

if there's no clear cut winner, then they play again until one person has the most cumulative wins after a round.

yes, it could go on forever, and while they're playing their silly RPS game, then I could sneak in and eat the cake from under them.

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Posted · Report post

I hope it's not an ice cream cake. If it is, it's all melty by now and nobody will want a piece after all.

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or you could play odd man out, then have the winners play each other...

eww.

melted ice cream cake

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