## Basket of colourful balls

There are two baskets containing the same number of balls. Each ball is either red or blue. The percentage of red balls in the first basket rounded off to the nearest tenth is 34.2%. The number of red balls in the second basket is 11. Which basket has more red balls?

[SOLVED]

#### Prasoon Gupta solved this puzzle:

The fraction of red balls is more than 13 but close to it. It implies that number of red balls / number of blue balls > 0.5 but very close to 0.5.

I am considering (r, b) = (x, 2x − 1) mix since this will make r / b closest to 0.5 when x is small.

Hence, x / 3x − 1 should be close to 34.2% and the smallest value of x for which it happens is x = 13. For higher number of red balls, we will need (x, 2x − 2) or even (x, 2x − 3).

#### Alex Yeilding solved this puzzle:

The first basket contains at least 13 red balls. No smaller number can be divided by an integer yielding an answer that rounds to 0.342.

#### Raj Kumar. V solved this puzzle:

The minimum number of red balls for which we can get the required 34.2% is 13 out of 38 balls. So, the first basket has more red balls.

#### Mark Cramer solved this puzzle:

The first value of n for which abs(round(n * 0.342) / n - 0.342) < 0.0005 is 38, with 13 red balls.

So the first basket has more red balls.

### Credit

This is an original puzzle from cotpi.