Plutonians have three feet. Suppose the Plutonian Orfkleeg has a box with an inf
ID: 3840313 • Letter: P
Question
Plutonians have three feet. Suppose the Plutonian Orfkleeg has a box with an infinite number each of red, blue, yellow, green, and white socks. Plutonian etiquette requires that Orfkleeg wear three socks of the same color. It’s dark, and Orfkleeg can’t see. What is the minimum number of socks Orfkleeg needs to take from the box to be ABSOLUTELY SURE there will be a suitable triplet of socks? This is a Discrete Math question and it is in the section where the pigeonhole principle is introduced, so I am assuming that it needs to be used.
Explanation / Answer
Pigeonhole principle in simple terms say that if we place n+1 objects in n boxes, then atleast one box must have more than one object. This is intuitive. Next we generalize it by saying that if we have n boxes and nk + 1 objects, then atleast one box contains more than k object.
Now in this question what we need is to get 3 ( ~"k") socks ( ~"object") of atleast 1 color ( ~"box" ). And in total we have 5 colors ( ~5 boxes ).
i.e. n=5, k=3 and this reduces to that we have 5 boxes and need 16 objects to have atleast one box containing more than 3 objects.
i.e. we need to draw 16 socks, so that there exist atleast one triplet.