New Contest: How Many Students in Ernestine Dubois Classroom?

I am sorry to announce that nobody found the correct answer to the first question

So, nobody will win this contest. See explanation at the end.

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Ernestine Dubois is a schoolteacher at the elementary school in the town of Trifouilly-les-Oies in France.

source

The policy of the town is to have classroom sizes between 17 and 35 students.

One day, Ernestine notices that if she chooses randomly two students in her classroom, there is exactly 50% chances that they will be of the same sex.

The question is: How many students in Ernestine classroom?

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To participate in this contest you need to reply before Sunday November 12th at 9AM (Pacific Time) with

1. the exact number of students in Ernestine classroom
2. an estimate of the $ value of this post as displayed on Steemit Tuesday November 14th at 9AM (Pacific Time)

Only one entry reply per person and no update. Anybody that sends several entry replies or updates their entry reply will be disqualified.
So, think carefully before answering: you have three days.

You can make as many non entry replies as you want.

The winner will need to answer accurately to 1 and be the closest for 2.

The prize will be the liquid award of this post.

Good luck. Start counting.

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Answer to the first question

Let B be the number of boys and G the number of girls in the classroom

The total number of students is then B + G

If there is 50% chance that two students randomly selected will be of the same sex, it means that the total number of pairs of students is double the number of pairs of students of the same sex. It is also double the number of pairs of students of different sexes.

The total number of pairs of students is (B + G) * (B + G - 1) / 2

The number of pairs of students of different sexes is B * G

So, we can write: (B + G) * (B + G - 1) / 2 = 2 * B * G
or
(B + G) * (B + G) - (B + G) = 4 * B * G
or
B² + G² + 2BG - 4BG = B + G
or
B² + G² - 2BG = B + G
or
(B - G)² = B + G
or
B + G = (B - G)²

So, we can see that the only solution is that the total number of students (B + G) is a perfect square.

As the total number of students needs to be between 17 and 35, the only solution is 25 students, as 25 is 5².

Unfortunately, nobody gives this answer. There were 5 answer for 24 and 8 answers for 26, but none for 25!