Hey dorks. A problem for you.
 

My pop once worked this out for me. Its a problem that he came up with after the classic "put the damn toilet seat down" argument with Mom.

The question is, which requires more work:
A. The man always puts the toilet seat down when he's done.
B. The man never changes the position of the toilet seat when he's done.

Some assumptions:
- The seat moving up and down both require the same amount of work, and should obviously be considered as 1 unit of work per movement.

- The woman must always have the seat down.

- The man must always have it down for the deuce, and up for peeing.

- There is exactly 1 man and 1 woman to the toilet seat.

- For the sake of argument, each pees 4 times a day, and drops off the kids 1 time per day.

- The order at which they use the toilet is completely random. The man could go all 5 times, then the woman the next 5, or any combination throughout the day.

If you want to change some of the variables to make the problem more interesting (I don't think its terribly difficult) feel free. I dunno if this is that interesting but alot of you guys flipped out over those physics problem. Maybe this will spark some interesting math stuff. Also, I'm a dork.

-Jihad

Re: Hey dorks. A problem for you.
 

Clearly B, common sense is enough to see that.

Re: Hey dorks. A problem for you.
 

To address that point, you can not argue common sense with women. In the heat of battle they revert to functional retards. You need an equation. Or a knife.

Re: Hey dorks. A problem for you.
 

The real question is....Why can't women put the toilet seat back UP?

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
The real question is....Why can't women put the toilet seat back UP?

[/ QUOTE ]

Because men would like to have sex again!

Re: Hey dorks. A problem for you.
 

Google this and you will find a program that simulates unisex bathroom usage by 100000 of people daily. B is the clear winner. Women need to quit bitching and put the seat down themselves.

Note: I put it down anyway because it looks ugly up.

Re: Hey dorks. A problem for you.
 

Link plz.

(I don't want to use google on my days off.)

Re: Hey dorks. A problem for you.
 

Shat. That pretty much ends it then if you link it. If they don't have the equation, that's what I'm interested in.

Re: Hey dorks. A problem for you.
 

I put not only the seat down, but also the seat cover, for one specific reason. Whenever you flush, toilet water sprays out, including piss and tiny pieces of poo. Mythbusters did an episode on this, and revealed that a toothbrush in a bathroom that didn't have a seat cover has a shitload (literally) more bacteria than a toothbrushg in a bathroom with a seat cover.

Re: Hey dorks. A problem for you.
 

i pretty much use a bathroom that is hardly ever used by the rest of my family. i usually leave the seat up but if i need to take a deuce i just put the toilet seat down. i do it without thinking twice and have never fallen into the toilet.

Re: Hey dorks. A problem for you.
 

As you worded it, the answer is clearly B.

If the man never changes the toilet position, the units of work used is exactly equal to the number of times that the position of the toilet is changed (let's call this value t).

If the man puts the seat down whenever he finishes and it is up, the number of units of work used is t (from the original problem) + 2*(the number of times that the man put the seat down and used the toilet to piss again before the woman has had to use it).

Please note: t is the same value in both situations.


The interesting question is what is more optimal to split the work 50/50, not what minimizes total work. Also, with different ratios of male:female.

But I have to eat dinner now.

Re: Hey dorks. A problem for you.
 

My family had a bathroom upstairs for the step-mom and step-sis, a downstairs bathroom for me and Dad. If I ever get married and have kids, this is the only acceptable option.

Re: Hey dorks. A problem for you.
 

Leave the seat down and piss in the sink. That way everyone is happy.

Re: Hey dorks. A problem for you.
 

A real man pees sitting down

Re: Hey dorks. A problem for you.
 

Thanks, now I have to drop a dugan.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
If the man never changes the toilet position, the units of work used is exactly equal to the number of times that the position of the toilet is changed (let's call this value t).

If the man puts the seat down whenever he finishes and it is up, the number of units of work used is t (from the original problem) + 2*(the number of times that the man put the seat down and used the toilet to piss again before the woman has had to use it).

Please note: t is the same value in both situations.

[/ QUOTE ]

I think this is incorrect.

For example, lets say we have 2 pees and 1 deuce for the male, and 3 uses for the female.

Now, look at the following possible combination:

DUDUDD

IE. The first user wants it down, second up, third down, fourth up and fifth and sixth up.

Under the strategy of always having it down, we have work of 2*t, where t = 2. Therefore, 4 units of work.

But, if we use the strategy of always leaving (we being guys), the work is:

1/3 (chance of seat being up at the start of the day) + 4.

Now, here, the strategy of always putting it down is actually better... but this only occurs when the day starts with a D, and we maximize the number of switches.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
I think this is incorrect.

For example, lets say we have 2 pees and 1 deuce for the male, and 3 uses for the female.

Now, look at the following possible combination:

DUDUDD


[/ QUOTE ]

This is pretty much the exact statement that I was hoping this thread would produce. Very funny, well put.

However, I would still like someone to do the work. I want to check mine.

Re: Hey dorks. A problem for you.
 

I say you slap the botch around until she learns to hover over the seat whenever she needs to use it. Over time, this will save loads of valuable energy.

Re: Hey dorks. A problem for you.
 

is this not insanely simple? leave the seat where it is when youre done. the seat only moves when its necessary. isnt that the least amount of work?

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
is this not insanely simple? leave the seat where it is when youre done. the seat only moves when its necessary. isnt that the least amount of work?

[/ QUOTE ]

No, the least amount of work is what my idea is.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
is this not insanely simple? leave the seat where it is when youre done. the seat only moves when its necessary. isnt that the least amount of work?

[/ QUOTE ]

But you need to prove it to a woman. Go.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
However, I would still like someone to do the work. I want to check mine.

[/ QUOTE ]

A quick way to look at it..

All of the outcomes when the male plays 'always put it down' have 8 work units (2 per U).

The WORST case scenario for the "always leave it" strategy occurs when:

The first play of the day is a D, and then ALL U's are followed by a D.

ie.

D,UD,UD,UD,UD,D (commas put in for clarity).

Now, the work function here = 2/5 + 8.

There are C(5,1) = 5 total ways to make this payoff.

That means, we are a total of (2/5 + 8)*5 - (8)*5 = 2
units of work above the average of the other strategy.

Which means we must simply find a set of combinations such that the sum of (8-payoff)*frequency is > 2. This is pretty simple to do.


Is this what you meant by check your work, or do you want an acutal payoff for the leave it strategy.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
[ QUOTE ]
If the man never changes the toilet position, the units of work used is exactly equal to the number of times that the position of the toilet is changed (let's call this value t).

If the man puts the seat down whenever he finishes and it is up, the number of units of work used is t (from the original problem) + 2*(the number of times that the man put the seat down and used the toilet to piss again before the woman has had to use it).

Please note: t is the same value in both situations.

[/ QUOTE ]

I think this is incorrect.

For example, lets say we have 2 pees and 1 deuce for the male, and 3 uses for the female.

Now, look at the following possible combination:

DUDUDD

IE. The first user wants it down, second up, third down, fourth up and fifth and sixth up.

Under the strategy of always having it down, we have work of 2*t, where t = 2. Therefore, 4 units of work.

But, if we use the strategy of always leaving (we being guys), the work is:

1/3 (chance of seat being up at the start of the day) + 4.

Now, here, the strategy of always putting it down is actually better... but this only occurs when the day starts with a D, and we maximize the number of switches.

[/ QUOTE ]

Your extra 1/3 is deceiving. You are making up "sessions" or "days". There is no difference in me pissing at 3PM or at 11:59PM, the beginning of a day is useless, it is all one long "session".

Because of this, there is only one starting position(not a daily one) The importance of this starting position approaches zero as toilet uses approaches infinity. Instead of going through the situation starting with both possibilities, let's say that it is the one that goes against my argument (it doesn't really matter). So let's say that "men always putting seat down after" is requiring one unit less at this point. Now every instance of "UU" in the sequence adds units of work (relatively) to the "men always putting the seat down after". For example, change your example by adding a "UU" in the middle and get DUUDUDD, if you recalcuate you get 6 compared to 4 1/3 (using your 1/3 theory instead of my worst case scenario one). Now this is not just another arbitrary example. It shows that if there is EVER a "UU" instance in the entire career of your toilet, then "leaving the toilet as is" requires less total work.

Re: Hey dorks. A problem for you.
 

B is clearly less work bc for A there will always be 8 units of work. 6 times w/ no work (5 chicks + 1 deuce) and 4 times w/ 2 (up and down) units of work. For B there will be anywhere from 1-8 units of work depending on the order in which it is used.

Re: Hey dorks. A problem for you.
 

you are a dork

Re: Hey dorks. A problem for you.
 

What do people think the goal should be? min( Work (male + female))? or min( difference( Work(male), Work(female)))?

I think it would probably be the latter, because its hard to convince someone that they should do more work than you just to minimize total work between the two of you. And convincing is what we are trying to do.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
Your extra 1/3 is deceiving. You are making up "sessions" or "days". There is no difference in me pissing at 3PM or at 11:59PM, the beginning of a day is useless, it is all one long "session".

Because of this, there is only one starting position(not a daily one) The importance of this starting position approaches zero as toilet uses approaches infinity.

[/ QUOTE ]

Im going to have to disagree here.

If you reread the question, you will see that it is in fact not one long session.

If it were one long session, then you simply set probabilites as given (U = 2/5 D = 3/5).


But, if we know the first action, for example, is D, the probability of the next action being D has gone down. That is, they are not independent.

You have to use the day adjustment because that is part of the question. You start the day with 10 options (6 Ds and 4 Us) and end it when we reach 0, then start again the next day.

Im not arguing its necessarily the best model for the problem (though it seems sufficient), but it IS the problem that was presented.

Re: Hey dorks. A problem for you.
 

You guys could show this argument to a woman but it wouldn't matter; putting the seat down after you flush is just the 'chauvinistic' thing to do.

Or you could just do th REAL manly thing and never lift the seat to pee. I mean come on, it's easy and sometimes fun to aim. Yup.

Re: Hey dorks. A problem for you.
 

I see, I interpreted it to mean some sort of distribution with daily averages approaching the above values as number of days approached infinity.

And yes, you are right about the days being in the OP now that I reread it, but I seriously doubt this is what the OP intended. He stated what he was trying to discern, and this model does not represent what he described.

Re: Hey dorks. A problem for you.
 

Who cares if the woman has extra work units to do - something they dont teach in math

Re: Hey dorks. A problem for you.
 

Whoa! I always assumed that this argument from the woman's perspective was based around aesthetics or cleanliness. I just talked to a woman about this after I was typing a response and she inquired what I was doing. She said basically that there were 4 possibilities (male poop, female poop, male piss, female piss) and that 3 of these required the toilet to be down. What the hell? Why is changing the toilet position after use so much easier than changing it before use?

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
Who cares if the woman has extra work units to do - something they dont teach in math

[/ QUOTE ]

lol

Re: Hey dorks. A problem for you.
 

Why would you pee with the seat up? That seems crazy, man.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
the classic "put the damn toilet seat down" argument with Mom.


[/ QUOTE ]

The last time this came up at MY house I said "we are both wrong", The lid AND seat need to be down after each use. Are we animals? After all we don't leave doors open and food lids off. CLOSE THE FREAKING LID, its there to be PUT DOWN when the toilet is not in use. When I walk in and the lid is up, I have something to bitch back about.

NOW, All of a sudden .....its no big deal if the seat is accidently left up.

Re: Hey dorks. A problem for you.
 

Leave it down, cleanliness is THEIR problem (after-all thay made the rule).

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
Leave the seat down and piss in the sink. That way everyone is happy.

[/ QUOTE ]

Correct answer. If dudes would just pee in the sink, no one would have to lift the seat ever. Plus, it saves water. It's good for the environment, and the marriage. A win-win-win situation!

Re: Hey dorks. A problem for you.
 

Interesting - I do simulations all day - might have to code this one up. Maybe even optimize it.

Re: Hey dorks. A problem for you.
 

The truely fair way to solve the toliet seat problem is to have everyone put the seat cover down when they're down with it. That way everyone has to lift it up to use it and everyone has to set it down when they're done. Everyone does the same amount of work per bathroom trip and the bathroom looks and is cleaner because the seat over is down.

Re: Hey dorks. A problem for you.
 

[ QUOTE ]
Leave the seat down and piss in the sink. That way everyone is happy.

[/ QUOTE ]

y not use the shower/tub. assuming this was in a full bath and not a half, i'd rather not move the urine closer to my toothbrush and other things that will get handled daily. this would also work better for kids who r not tall enough to have mr johnson at just above counter-level. teach them early and they r set for life.

Re: Hey dorks. A problem for you.
 

All this math is fun and good but do you think any woman would actually be able to understand it?