It's dark. You have ten grey socks and ten blue socks you want to put into pairs. All socks are exactly the same except for their color. How many socks would you need to take with you to ensure you had at least a pair?

3 socks

Step-by-step explanation:

Let's look at what outcomes you can have when you take one sock at a time for the first three picks.

First pick:                      grey

You have:                    1 grey sock

Second pick:         grey or blue

You have:                     1 grey sock & 1 grey sock (a pair)

                                or 1 grey sock and 1 blue sock (no pair)

Third pick:                grey or blue

You have:                 2 grey + 1 grey (1 pair)

                                or 2 grey and 1 blue (1 pair)

                                or 1 grey sock, 1 blue sock, 1 grey (1 pair)

                                or 1 grey, 1 blue, 1 blue (1 pair)

Notice that obviously after the first pick, you cannot have a pair since you only took out one sock. After the second pick, you may or may not have a pair. After the third pick, you must have a pair.

3 socks

I think the answer is 4, you can't be sure with two

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3