The Great Houdini is performing again! A guy from the audience arbitrarily chooses $52$ cards from a huge stack. He shuffles the cards and announces to Houdini that there are $a$ spades, $b$ hearts, $c$ clubs and $d$ diamonds. Houdini now has to guess the suits in the deck one by one. After every guess, the guy from the audience reveals the current card and everybody (including Houdini) sees the correct suit.
Houdini's strategy: At any moment in time, Houdini knows the numbers of remaining suits in the deck. Houdini always guesses a suit that occurs the highest number of times (ties are broken arbitrarily).
Question: What is the smallest possible number of correct guesses under Houdini's strategy (over all possible values of $a,b,c,d$)?
Answer
The smallest possible of correct guesses is max(a, b, c, d): every other suit could come up first and he would guess the most likely one over and over until nothing was left but those, and then he would get all the rest correct.
No comments:
Post a Comment