You have 20 red balls, 14 blue balls. You draw out balls, 2 at a time. If they are of same color, add a blue ball the pile. If the are of different colors, add a red ball to the pile. (i) will the color of the last call left be unique ? (ii) if yes, then what's the color ?

Question

Accepted Answer

Drawing balls and adding to pile based on color. Will the last ball left be unique and what color?

Drawing 2 balls at a time and adding to pile based on color
If same color, add a blue ball. If different color, add a red ball
Question asks if last ball left will be unique and what color it will be

Accepted Answer

Initial Setup:
Red Balls: 20

Blue Balls: 14

Rules:
Two balls of the same color: Add one blue ball.

Two balls of different colors: Add one red ball.

Key Observation:
Every time you draw balls:

Two Red Balls → +1 Blue Ball: Red balls decrease by 2, blue balls increase by 1.

Two Blue Balls → +1 Blue Ball: Blue balls decrease by 1.

One Red and One Blue → +1 Red Ball: Red balls stay the same (effectively), blue balls decrease by 1.

Parity Analysis:
The number of red balls changes its parity (even/odd) only when an odd number of red balls are removed.

Drawing one red and one blue ball maintains the parity of the red ball count (remains even in this case since 20 is even).

Drawing two red balls (removing an even number of red balls) changes the parity of the red ball count.

Given the above rules, we start with an even number of red balls (20). The parity remains the same (even) when drawing one red and one blue ball or when drawing two blue balls.

Conclusion:
We can draw two blue balls (and replace with one blue) until no blue balls are left. In this scenario, we keep the even parity of red balls.

When only one ball remains:

The red ball's even parity means all blue balls are exhausted or remaining operations don't affect the final single ball.

With even remaining red balls and no blue balls, the last remaining ball must be a red ball.

Answers:
(i) Will the color of the last ball be unique? Yes, the color will be unique.

(ii) If yes, then what's the color? The color of the last ball will be red.

If you have more puzzles or need further clarifications, feel free to ask! 😊

You have 20 red balls, 14 blue balls. You draw out balls, 2 at a time. If they are of same color, add a blue ball the pile. If the are of different colors, add a red ball to the pile. (i) will the color of the last call left be unique ? (ii) if yes, then what's the color ?

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