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Colour of the Last Ball

You have a bag with 20 blue and 13 red balls.
Your task is to pick two balls in succession.
If the balls are the same colour then you remove them and replace them with a blue ball.
If the balls are of a different colour then you remove them and replace them with a red ball.

What is the colour of the last ball?

Solution

The last ball will always be red.
We need to apply the concept of odds and evens in this puzzle.

For instance, you pick a red and blue ball, you will place the red ball back inside.

As there are 13 red balls, they will be in odd numbers.
Hence, the last one will be a red ball.