Memory Match Problem #2
You are playing a game of memory match with 3 of your friends (4 players total).
To begin, you have arranged 50 pairs of cards randomly on the table (100 cards total). As you start to play, you begin to wonder when you can say for sure that you were going to win.
So, what is the minimum number of matching pairs that you would have to find to guarantee that you win?
This problem is a part of the Memory Match Problem Series
The answer is 26.
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1 solution
To find this minimum number of matching pairs, we must examine the worst-case scenario. This would be if 2 of the other players did not get any matches, thus enabling the third friend to get as many matches as possible.
Now we must simply determine the number of matches we have to obtain in order to beat this third friend. Obviously, if we got 25 matches and our friend got 25 matches, we would only tie. Thus, in order to ensure a win, we must get a minimum of 2 6 matches.