Arcade House Party Conundrum

[Weehawk]

Jason and Anna Cram went to an arcade party where they and four other married couples were the only people present.

Some of the people at the party had met before, some had not. During the course of the evening, each pair of people that had not met previously made it a point to play a game of Donkey Kong together. No other Donkey Kong was played.

At the end of the party, Jason asked everyone in attendance, including Anna, how many people they played Donkey Kong with. To his surprise, Jason got a different answer from each person.

How many people did Anna play Donkey Kong with at the party?

For the first person who can post the correct answer with an explanation why it is correct who does not already have one, I have a t-shirt:



Please recuse yourself if you were already familiar with the problem.

If you already have the shirt, you can PM your answer to me and I will credit you in the thread.

[ChrisP]

Are you positive that there isn't a piece of information missing here?

"Someâ„¢" had or had not met before...

[ChrisP]

[homerwannabee]

6?

Edit:  Too stupid to see the explanation thing.  Suck!

[ChrisP]

Here's what I have so far and I don't even know if I'm on the right track at all, so somebody can take this and run with it, fttt this I'm gone.

- There are 10 people total
- The maximum number of people each individual could play DK with is 8 (since they would definitely know themselves and their spouse, but could potentially not have met any of the others).
- The question says that *each* person gave Jason a different answer. I interpret that to mean that he got 9 *distinct* answers (that is, nobody's answer was the same as anybody else's answer).
- There are 9 possible answers, zero through 8.
- However, zero AND 8 could not have BOTH been given as answers. One or the other is possible, but not both. If an attendee played zero games, it means they knew everybody at the party, which means that there could not have been an attendee who played 8 games, because you can't simultaneously have a person who has met everybody and a person who has met nobody.
- So Jason only could have gotten 8 distinct answers.

That's where I'm stuck, and I haven't even gotten to how Anna's answer could be narrowed down from the information given.

[homerwannabee]

Here's what I have so far and I don't even know if I'm on the right track at all, so somebody can take this and run with it, fttt this I'm gone.

- There are 10 people total
- The maximum number of people each individual could play DK with is 8 (since they would definitely know themselves and their spouse, but could potentially not have met any of the others).
- The question says that *each* person gave Jason a different answer. I interpret that to mean that he got 9 *distinct* answers (that is, nobody's answer was the same as anybody else's answer).
- There are 9 possible answers, zero through 8.
- However, zero AND 8 could not have BOTH been given as answers. One or the other is possible, but not both. If an attendee played zero games, it means they knew everybody at the party, which means that there could not have been an attendee who played 8 games, because you can't simultaneously have a person who has met everybody and a person who has met nobody.
- So Jason only could have gotten 8 distinct answers.

That's where I'm stuck, and I haven't even gotten to how Anna's answer could be narrowed down from the information given.

What you said, and my answer is 7

since 0 and 8 can't be given as answers.   

[VON]

Chris, we seriously have to stop meeting like this   I'll type faster next time...

If I'm reading this correctly...

Jason asked everyone in attendance how many people they played Donkey Kong with, and got a different answer from every person.

There were 10 people in total at the event, or 5 couples, which means the most number of different people any one person could have played with is 8 (because you can't play with yourself or your partner).

Thus, for Jason to have received 9 different answers, those answers must have been 8,7,6,5,4,3,2,1, and 0.

However, if someone played with 0 other people, then suddenly the maximum number of different people any one player could have played with becomes 7, and the problem no longer makes sense.

So, what am I misinterpreting about the Arcade House Party Conundrum?

[Weehawk]

Here's what I have so far and I don't even know if I'm on the right track at all, so somebody can take this and run with it, fttt this I'm gone.

- There are 10 people total
- The maximum number of people each individual could play DK with is 8 (since they would definitely know themselves and their spouse, but could potentially not have met any of the others).
- The question says that *each* person gave Jason a different answer. I interpret that to mean that he got 9 *distinct* answers (that is, nobody's answer was the same as anybody else's answer).
- There are 9 possible answers, zero through 8.
- However, zero AND 8 could not have BOTH been given as answers. One or the other is possible, but not both. If an attendee played zero games, it means they knew everybody at the party, which means that there could not have been an attendee who played 8 games, because you can't simultaneously have a person who has met everybody and a person who has met nobody.
- So Jason only could have gotten 8 distinct answers.

That's where I'm stuck, and I haven't even gotten to how Anna's answer could be narrowed down from the information given.

What you said, and my answer is 7

since 0 and 8 can't be given as answers.   

The answer is incorrect, and the reasoning you borrowed is fatally flawed.

[The Pro]

It's a classic arcade party so obviously there's a few liars and cheats in there, it won't add up.

[ChrisP]

[Weehawk]

It's a classic arcade party so obviously there's a few liars and cheats in there, it won't add up.

I naively overlooked this. In my fictional scenario everyone told the truth.

[VON]

I've got it!

One of the party goers was a schizophrenic having an episode who either played with themselves or their partner.

T-shirt me baby!!

Or  was on the scene, flying solo.

Boom!  T-shirt me again

[Weehawk]

Or  was on the scene, flying solo.

 

[Barra]

You say:

"At the end of the party, Jason asked everyone in attendance"

Can we make any assumption that not everyone was still at the party when Jason asked?

[Weehawk]

You say:

"At the end of the party, Jason asked everyone in attendance"

Can we make any assumption that not everyone was still at the party when Jason asked?

No. He asked everyone who attended. Nobody left before he asked.