We have a bag filled with 201 marbles, of which100 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 intothe bag. If the two marbles are of different colors, we remove the two marbles and add a redmarble into the bag. What is the color of the last marble in the bag?

The answer is that the last marble is red.

Step-by-step explanation:

The answer is that the last marble is red.

We can justify this answer by denial:

For the last marble to be blue, at some stage in the extraction of marbles there must have been n blue marbles and one last red marble.

To remove that red marble, it has to be extracted in one of the following rounds.

If the last red marble is removed, the other marble extracted will be a blue one. Since the marbles extracted are of different color, according to the rules, a red marble must be incorporated into the bag.

So the amount of red marbles in the bag cannot decrease to less than one.

For this reason the last marble is red.