A box contains 12 marbles of three different colors – Green, Yellow and Blue – 4 of each.
If you were to close your eyes and pick them at random, how many marbles must you take out to be sure that there are at least two of one color among the marbles picked out ?
(In reply to
Puzzle Answer by K Sengupta)
Let green marble, yellow marble and red marble be respectively denoted by G,Y and B.
The individual cannot pick 1 marble for obvious reasons.
If the individual picks 2 marbles, then (disregarding permutations), three of the available possibilities may be GY, GB, or YB. So two marbles possess different colours. Contradiction.
If the individual picks 3 marbles, then disregarding permutations, one of the possibllities is GYB. So, all 3 marbles will be coloured differently. Contradiction.
If the individual picks 4 marbles. Since the available colours are 3, the can be at most 3 differently colored marbles,. In such a situation, the 4th marble will always duplicate one of the available colours. For example, it is possible to have:
GYBG, GYBY, GYBB etc.
Consequently, the required minimum number of marbles is 4.
Edited on March 4, 2022, 1:01 am
Explanation for Puzzle Answer
