PigeonHole Principal

Question

A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?

Comments

Ans should be 3

---

No

---

sorry sorry it should be 14 :p , I didn't read carefully

---

Please Explain

Answer 1

Without Directly using Pigeon Hole Principle , an intuitive way  would be :

Given 12 Black and 12 Brown socks . In order to take out at least 2 Black socks , in worst case first we need to take out 12 shocks (which might end up Brown in worst case), then take out 2 socks (which would be definitely black) . Thus we need to take out total 14 socks

Comments

Well if u assume that there were 12 socks of each color then it will be a piece of cake question. My question is why 12 ? I could have assumed something else ?

---

@na462 in question it is given, a dozen of brown and a dozen of black.

1 dozen = 12 pieces

Answer 2

According to ques, there are 12 black and 12 brown socks.

In order to take out 2 black socks, lets consider what might be the worst case.

I pulled out 1st and it turned out to be brown, then i took 2nd and it also turned out to be brown. Doing so till 12th sock, it turned out all brown socks. But now all brown socks are over and black socks are left only. So the next 2 socks would be black for sure. Hence total attempts in order to take out at least 2 black socks are 14.