Puzzle
There are 20 red balls and 16 blue balls in a bag. Any 2 balls are removed at each step and are replaced with a new ball on the basis of the following conditions:
If they are of the same color, then they are replaced by a red ball.
If they are of different colors, then they are replaced with a blue ball.
Find the last ball to remain after the entire process.

Question

Puzzle

There are 20 red balls and 16 blue balls in a bag. Any 2 balls are removed at each step and are replaced with a new ball on the basis of the following conditions:
If they are of the same color, then they are replaced by a red ball.
If they are of different colors, then they are replaced with a blue ball.
Find the last ball to remain after the entire process.

Accepted Answer

Blue balls can only be reduced by two and that too if the 1st condition is satisfied, i.e., if you choose both blue balls, then they are replaced by a single red ball. In no other ways you can reduce blue balls. Red balls can be reduced by one on the basis of 2nd condition if you choose both different balls and on the basis of 1st condition if you choose both red balls.
Now, because there are an even number of blue balls and blue balls can only be reduced by two, you will end up with either 0 or 2 or 4...(even number) blue balls in the bag at any point during the replacement process. There will never be a situation in which the bag contains an odd number of blue balls. As a result, the last ball in the bag will be a red ball in any combination of replacements.

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