Question

We have a bag filled with 201 marbles, of which 100 of them are blue and 101 of them are red. Every turn, we remove 2 marbles from the bag. If the two marbles are of the same color, we remove the two marbles but add a blue marble into the bag. If the two marbles are of different colors, we remove the two marbles and add a red marble into the bag. What is the color of the last marble in the bag?

Answer 1

Red Marble is the color in the bag

Explanation:

Total number of marbles ; 201

number of red marbles ; 101

number of blue marbles ; 101

• Every turn, 2 marbles of the same color are removed, and add a blue marble

• if two marbles are different color are removed , and add a red marble

• From the analysis of the question; there are three possibilities;

first possibility ; From what is said as the condition, it can be inferred that the number of blue marbles is reduced by a factor of 1 , while the number of red marbles remains constant. this shows that the two marbles of the same color that was removed is most likely BLUE.

Second possibility ; Two red marbles are added (of the same color) and add a blue marbles, implies the the red marbles reduce by a factor of 2 while the blue marbles increase by a factor of 1. this is also possible.

Third possibility ; Two marbles of different color implies 1R and 1B , and then a red marble is added. this shows that the number of red marble still remains constant ( 1R removed, 1R added), while the number of blue reduce by 1 ( remove 1B, and not replaced back).

From the various possibilities, it can be inferred that the number of red marbles is either increasing by a factor of 2 or remains constant. this further shows that in all three , 1R marble will always remain in the bag no matter the possibility as such in all three scenerios, it further shows that if there is only a marble remaining, it would have been the RED MARBLE WHICH IS AUTOMATICALLY THE LAST MARBLE from the analysis done above.