Question

There are 12 of the zodiac. how many people are needed to guarantee that at least six of these people have the same sign? your answer must be one integer.

Answer 1

Answer:es, the answer is 61. This is related to a mathematical principle called the Pigeonhole Principle, which states that if you are trying to sort  n+1  objects into k sets (where nk=r;n,k,r∈Z+), at least one set must contain at least r+1 objects. (This can be proven by proof by contradiction, but is pretty standard and so generally can just be used as justification of an answer by itself.)

For your problem, you have 12 signs of the zodiac - these are your 12 sets (so k=12). You are looking to find how many it takes before a set contains 6 objects (so r+1=6 and thus r=5). Therefore, n+1=r×k+1=12×5+1=61.

Explanation: