Pigeon Hole Principle question: You need to find three matching color socks from
ID: 3027470 • Letter: P
Question
Pigeon Hole Principle question:
You need to find three matching color socks from a drawer with an infinite number of socks in 5 difference colors (red, blue, yellow, green, white). What is the minimum number of socks needed to be taken (you cant tell what color they are when they are taken from the drawer) from the drawer to find 3 that match?
My answer is 3 since you could select 3 socks of the same color in a row. However, since this is a pigeon hold principle problem, I think the answer may actually be 6 since after 5 selections the 6th sock will have to match one of the previously selected sock colors.
Please help.
Explanation / Answer
As the Socks have 5 different colors (red, blue, yellow, green, white),
If five socks are drawn then they might be these five different colored socks, so we don't have a pair of match in such case. When the sixth sock Is drawn this will be one of the five socks and we have a match. Say White, white,
To get the second match we draw another sock and we may have another match, say yellow, yellow
to obtain the third match we draw the 8th sock say red, red
Hence by Pigeon Hole principle atleast 8 socks are to be drawn to be sure of drawing three matches.