Color of Next Ball Puzzle-Asked in Interviews.

Question:

You have 20 blue balls and 14 red balls in a bag.
You put your hand in and remove 2 at a time.

If they’re of the same color, you add a blue ball to the bag.

If they’re of different colors, you add a red ball to the bag.

( Assume you have a big supply of blue & red balls for this purpose).

Note: When you take the two balls out, you don’t put them back in, so the number of balls in the bag keeps decreasing.

What will be the color of the last ball left in the bag?

Solution: Blue

There are 3 possible cases of removing the two balls:-
a) If we take off 1 RED and 1 BLUE, in fact we will take off 1 BLUE
b)If we take off 2 RED, in fact we will take off 2 RED (and add 1 BLUE)
c) If we take off 2 BLUE, in fact we will take off 1 BLUE
So In case of (a) or (c), we are only removing one blue ball, but we always take off red balls two by two.
If there are 14 (even) number of red balls, we can not have one single red ball left in the bag, so the last ball will be blue.

Thanks for Reading

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