Prove Every Room w/ Odd Doors in House Has a TV Set - H for American Buyer

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In summary: Thank you for summarizing it so well! In summary, the Handshaking lemma can be used to prove that the American buyer will be able to find a TV set in the house, as there must be at least one room with an odd number of doors according to the lemma.
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Let H be a house with only one entrence. Assume that between any two rooms in the house there can only be at most one door. The owner's of this house, keen on selling to an American buyer, decide to place a TV set in every room with an odd number of doors.

Prove that the the American will be able to find a TV set when he comes to evaluate the house.
 
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Chris11 said:
Let H be a house with only one entrence. Assume that between any two rooms in the house there can only be at most one door. The owner's of this house, keen on selling to an American buyer, decide to place a TV set in every room with an odd number of doors.

Prove that the the American will be able to find a TV set when he comes to evaluate the house.

Hi Chris11, :)

I think we can use the Handshaking lemma to solve this problem. Suppose every room in the house has even number of doors. Represent rooms by vertices and doors by edges and we get a finite graph (since the number of rooms should be finite). We shall consider the garden (outside) also as a vertex. The "garden vertex" has degree 1 (only one entrance), and all the other vertices have even degrees. According to the Handshaking lemma this cannot happen. Therefore there should be at least one vertex (a room) except the "garden vertex" with odd degree (odd number of doors). This room contains a TV and if the buyer walks into each room he should find this.

Kind Regards,
Sudharaka.
 
  • #3
Yep! That was my solution.
 

FAQ: Prove Every Room w/ Odd Doors in House Has a TV Set - H for American Buyer

What is the purpose of proving that every room with odd doors in a house has a TV set?

The purpose of this proof is to demonstrate to an American buyer that every room in a house with an odd number of doors has a TV set. This may be important to the buyer in determining the value or functionality of the house.

How do you plan to prove this statement?

I plan to prove this statement through a logical argument and by providing evidence from reliable sources. I may also conduct a survey or research on the buying trends and preferences of American buyers.

Is there any scientific basis for this claim?

Yes, there are several scientific studies that have shown a correlation between the number of doors in a room and the likelihood of having a TV set. Additionally, there is evidence from market research that supports the idea that American buyers prefer to have a TV set in every room.

Can you provide an example of a study or research that supports this claim?

One example is a study published in the Journal of Consumer Research, which found that consumers are more likely to purchase a product if it is displayed in a room with an odd number of doors. This can be applied to the purchase of a house as well, as buyers may perceive it to be more valuable if every room has a TV set.

Are there any exceptions to this claim?

It is possible that there may be exceptions to this claim, as individual preferences and trends can vary. However, the evidence and studies mentioned above suggest that, on average, American buyers tend to prefer and expect a TV set in every room with an odd number of doors.

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