You have 20 blue balls and 13 red balls in a bag. You put your hand in and remove 2 at a time. If theyre of the same color, you add a blue ball to the bag. If theyre of different colors, you add a red ball to the bag. Assume you have a big supply of blue & red balls for this purpose.
Answers
The last ball in the bag will be red.
Given:
Total number of blue balls = 20
Total number of red balls = 13
Balls removed at a time = 2
To Find:
The colour of the last ball in the bag
Solution:
There are three possible cases of removing the two balls -
1 ) If we remove 1 Red and 1 Blue, we will actually remove 1 Blue.
2 )If we take off two reds, we will indeed take off two reds (and add 1 Blue)
3 ) If we remove 2 Blue, we will really remove 1 Blue.
In cases 1 and 2, we only remove one blue ball, but we always remove two red balls at a time.
Now,
Because the number of red is odd, thus, there will be just one red ball in the bag with other blue balls.
Removing one red and one blue ball will result in just removing the blue ball.
Answer: The red ball will be the bag's final ball.
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