# Problem of the Day: 1/13/13

Jemma’s sock drawer is a mess. She has four types of socks—four pairs each of pink, navy with yellow stripes, black with polka-dots, and purple/green argyle—all jumbled up together. Her dress principles require that she always wear two socks of different colors, however. How many socks must she pull out randomly in the morning to ensure that she gets two socks of different colors?

Solution to yesterday’s problem:
To solve an equation with absolute value, you must know this: for an absolute value to equal something, the original number can be the positive value or the negative value. For instance, if $|x-2|=1$, then x – 2 = 1 or -1.

In this equation, we have two absolute values. So first let’s remove the absolute value and create our two cases:

(1) $|x-1|-2=1$

(2) $|x-1|-2=-1$

Before we remove the absolute value in either case, we must isolate it on one side. Here, we add 2 to both sides:

(1) $|x-1|=3$

(2) $|x-1|=1$

Now we can work on each case individually. Let’s remove the absolute value in case 1 first:

(1a) $x-1=3$

(1b) $x-1=-3$

Solving each of these like a normal equation, x = 4 or x = -2. Moving to the second case, we’ll remove the absolute value first:

(2a) $x-1=1$

(2b) $x-1=-1$

Solving, we get x = 2 or x = 0. So our solutions are 4, -2, 2, and 0. Adding these up, we find the answer to be 4.