# Which colour is the last ball

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There is a bag with 20 black 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 black ball. If the balls are of different colour then you remove them and replace them with a red ball. What is the colour of the last ball ?

SherlockHolmes Expert Asked on 11th November 2019 in

There are three options when picking balls.

1) You pick 2 black balls. You remove them and replace them with one black ball. The total amount of black balls will decrease by 1 and the number of red balls stay the same.
2) You pick 2 red balls. You remove them and replace them with one black ball. The total amount of black balls will increase by 1 and the number of red balls will decrease by 2.
3) You pick a black and a red ball. You remove them and replace them with one red ball. The total amount of black balls will decrease by 1 and the number of red balls stay the same.

The number of red balls will always decrease by an even number (0 or 2).
The starting number of red balls is odd (13) and it will stay odd when you decrease it by an even number. So the number of red balls will never be 0.

The last ball will always be red.

CugelTheWise Expert Answered on 11th November 2019.

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