If you have adjacent rooms with a door between them, does that count as one door or two? I mean, it would have to count as a door for room A and a door for room B even though it's a single door, wouldn't it?
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Actually, they are only counted once. If you saw a door connecting two rooms in real life, you wouldn't say "there are two doors".
Sorry if this was unclear.
+118673 Actually, they are only counted once. If you saw a door connecting two rooms in real life, you wouldn't say "there are two doors".
This is not true.
You stand in the lounge room. All the doors are shut and you think to yourself, this room has 4 doors.
You walk into the bedroom and close the connecting door. Then you say to yourself this room has 2 doors.
The fact is that one of those doors has been counted twice.
The lounge room has in facts just one side of 4 different doors and the bedroom has one side of 2 different doors.
Yes, but we are considering the house as a whole. Imagine a bird's eye view of the house with a transparent roof so that you can see all the doors.
If a house had two rooms with a door connecting them (and that's it), would you say there are two doors?
+118673 Yes, but we are considering the house as a whole. Imagine a bird's eye view of the house with a transparent roof so that you can see all the doors.
That is rubbish.
The questions says, and I quote "every room has an even number of doors"
Each room is being considered independently of the other rooms.
It is not being viewed as bird's eye view whatsoever.
+118673 Problem: Suppose we have a house (with finitely many rooms) in which every room has an even number of doors. Prove that the number of doors from the house to the outside world is also even.
I will assume that there are no doors to cupboards. All doors go either to another room or to outside.
My logic on this is quite simple. 
I expect you want me to look at your logic. Maybe I will do that afterwards.
Let 2n be the number of internal door SIDES.
Let k be the number of external door sides.
The number of door sides altogether is 2n+k
Every door has 2 sides so the number of doors is (2n+k)/2 = n+k/2
There must be a whole number of doors so k must be divisable by 2
therefore
If there is an even number of doors in each room then there must be an even number of doors going outside as well.
+118673 "Thanks for any answer I may receive, as I understand this post is long.
For anonimity reasons, I might delete this later. I hope you're ok with that."
No it is absolutely not ok to delete your question.
That just means that you are worried that your teacher will see that you are cheating.
+118673 I have decided to leave my answer visable because you have made an attempt at the question and I have not found your error that you are supposed to find for yourself.
And
I know answers similar to mine would be all over the internet. It is a common question.
i am not rogr
+118673 No good teacher would ever mind being questioned in this way.
It is not a matter of distrust. You teacher does not want you to blindly believe what he/she says.
Mathematics requires understanding, not blind faith. !
+93 Melody, I understand your point of view but lets not just assume that they are "cheating", just by wanting to delete the question.
What the fuck doorknoob?! Why do you feel the need to inject your opinion on this post or any other?
The asshole has already deleted his question. This post is now useless for anyone wanting to do research on this question.
“nevermind i got it” means he got his rocks off, but he’s a selfish dick and doesn’t want to return the favor.
