Puzzle | Black and White Balls

You have 20 white and 13 black balls in a bag. You pull out 2 balls one after another. If the balls are of same color, then you replace them with a white ball – but if they are of different color, you replace them with a black ball. Once you take out the balls, you do not put them back in the bag – so the balls keep reducing. What would be the color of the last ball remaining in the bag.


Solution: Black
This puzzle looks like a difficult one, till you find out the solution. But, the minute you get the solution, you feel that this was dead simple. If you pull out 2 black balls, you replace them with a white ball. On the other hand, if you pull out one black and one white – you replace it with a black ball. So, the black balls would always be odd in numbers – either you remove 2 together or remove 1 and add 1 – so they remain odd always. Hence, the last ball to stay in the bag would be a black ball.

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