# Fifty Shades of Gray (Socks)

Heidi has a huge drawer full of gray socks. These socks are all disorganized in a random heap. As the title of this puzzle suggests, there are fifty different shades of gray sock in her collection (it’s assumed that it is a huge pile of socks, so there could be multiple copies of every shade).
Heidi has a great eye for color, but not perfect. She can distinguish the shade of socks only if they differ by two, or more, shades. So, if a pair of socks is in the range ±1 they appear the same color to her.
Heidi’s desire is to find a pair of ‘matching’ socks (two socks that are no more than one unit shade apart) but, unfortunately, she is currently blindfolded (don’t ask). How many socks does Heidi need to take from the drawer to guarantee that she has at least a pair of ‘matching’ socks?
As a bonus, Heidi would like to find a pair of matching socks for her partner too. How many additional socks will she need to pull to ensure that she gets at least two pairs of ‘matching’ socks?