Fernando wears three colours of socks: red, blue and white. He doesn't pair his socks when he washes them, he just throws them into his sock drawer.
A.) What is the fewest number of socks Fernando needs to take out of the drawer to guarantee he has a matching pair? Explain.
B.) Is there a fewest number of socks he could take out to guarantee that he will have a red pair? Explain.
(A) 3 colors, so 4 socks must have two the same
(B) Depends on how many pairs of each color. Worst case is if there is only one red pair. Then he might need to take them all.
A.) To guarantee that Fernando has a matching pair of socks, he needs to take out at least three socks from the drawer. Here's the explanation:
Since Fernando wears three different colors of socks (red, blue, and white), the worst-case scenario is that he picks one sock of each color in the first three attempts. In this case, he wouldn't have a matching pair yet. However, on his fourth attempt, no matter which color sock he picks, he is guaranteed to have a matching pair. This is known as the Pigeonhole Principle.
So, the fewest number of socks Fernando needs to take out of the drawer to guarantee he has a matching pair is three.
B.) Yes, there is a fewest number of socks Fernando could take out to guarantee that he will have a red pair, and that number is four. Here's why:
In the worst-case scenario, Fernando picks one red sock and two socks of different colors in his first three attempts. In this case, he still doesn't have a matching pair of red socks yet. However, on his fourth attempt, no matter which color sock he picks, he is guaranteed to have a red pair of socks.
Hence, the fewest number of socks Fernando needs to take out of the drawer to guarantee he has a red pair is four.