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Logic Problem

Logic Problem Solution - 10 December

There is a bag which have 21 blue balls and 23 red balls. You also have 22 red balls outside the bag.

Randomly remove two balls from the bag.
* If they are of different colors, put the blue one back in the bag.
* If they are the same color, take them out and put a red marble back in the bag.

Repeat this until only one marble remains in the bag.


What is the color of the sole marble left in the bag ?

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Solution
The last marble will be blue.

Since balls can only be taken out in pairs and you started off with an odd number of blues there is always going to be one blue left over that you'll keep putting back in the box until it's left on it's own