Given:
Number of black marbles = 6
Number of white marbles = 6
Let's determine the least number of marbles that can be chosen to be certain that you have chosen two marble of the same color.
To find the least number of marble to be chosen to be cartain you have chosen two marbles of the same color, we have:
Total number of marbles = 6 + 6 = 12
Number of marbles to ensure at least one black marble is chosen = 6 + 1 = 7
Number of marbles to ensure at least one white marble is chosen = 1 + 6 = 7
Therefore, the least number of marbles that you must choose, without looking , to be certain that you have chosen two marbles of the same color is 7.
ANSWER:
7
I believe the phi ratio^2 = 1 + phi ratio
phi ratio = 1.6180339
phi ratio^2 = 2.6180339
