Jason had a lot of socks in his sock drawer — 25 white socks, 10 red socks, 12 blue socks, 3 rainbow socks, 3 green socks, 7 purple socks. He forgot to pack his socks for the field trip, but he was already late, so he decided to just grab some number of socks and just go.To not wake up his sister, he had to do it in the dark so he couldn’t see the color.What is the minimum number of socks he needed to grab to guarantee at least 5 matching pairs of socks?

 Feb 24, 2021

Let's have him get his first $4$ pairs from white, red, blue, rainbow. Then we have to pick as many socks as possible without getting another pair. I will take a green sock, a purple sock, and another white, red, blue, and rainbow sock. Now, the next sock I pick, I am guaranteed to get another pair. So far, I have picked $4*2+6=14$ socks. The answer is $14+1=\boxed{15}$ by the pigeonhole principle. 

 Feb 24, 2021

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