I am bored, here's a question for you guys:
I'm a shady card dealer with a deck of cards. In the deck there are 5 different types of cards. The way this card game works is you win if you have a hand you can play. There are only 2 types of hands: 5 of a kind, or one of each kind. Since im shady, I will make sure you don't have a hand, but after a certain number of cards 'n' has been given to you, no matter how I act, you will always have a hand. What is the smallest number 'n' for which this is true?

Question

I am bored, here's a question for you guys:
I'm a shady card dealer with a deck of cards. In the deck there are 5 different types of cards. The way this card game works is you win if you have a hand you can play.  There are only 2 types of hands: 5 of a kind, or one of each kind.  Since im shady, I will make sure you don't have a hand, but after a certain number of cards 'n' has been given to you, no matter how I act, you will always have a hand.  What is the smallest number 'n' for which this is true?

anonymous · Answer

Pretty sure it's 17.

anonymous · Answer

the smallest number possible is 9. (gotta love the pigeon-hole theorem)

anonymous · Answer

Hrm.. Did I misunderstand the question?

anonymous · Answer

hmm..how so 17? i could be wrong

anonymous · Answer

i believe its 17, because if im shady and hand out 16, i could give you 4 of 4types of cards

anonymous · Answer

well the way i figure, if you have 9 cards, you have to have either 5 of one kind, or one of each. ok, i'm wrong

anonymous · Answer

Right.

anonymous · Answer

true story, sitting on my butt all day has made my brain mush

anonymous · Answer

Ok, back to mine now ;)

anonymous · Answer

as soon as i hand out that 17th card, it will either be one of the 4 types you already have (which makes 5 of a kind), or it will be the last type (with makes one of each kind)