Monday mystery- 12-2-24 -- answer

[Ittermat]

This weeks mystery!

Taken from  my sherlock holmes mystery cards
   
The problem:

"I heard of a schoolmistress, down in Catford, with a rather peculiar morning ceremonial." Holmes told me. "It is her habit" He continued, "to start the school day with a series of polite bows. Each boy mush bow to each other boy, and then to each girl, and then to the teacher. Likewise each girl must bow to each other girl, then to each boy, and then to the teacher. The whole process requires 900 obeisances. If i tell you that there are twice as many girls in the school as boy, you will undoubtedly be able to tell me how many boys there are."

"undoubtedly" I replied drily.

Can you solve the issue?

The Answer: 

The teacher, who does not bow back, serves to counterbalance the fact that each child is not required to bow to his or herself. There are 900 bows, and each child bows once for each other, so there are 30 children, as the square root of 900. As one third are boys, then there are 10 boys and 20 girls.
       

No winners!


***Collect your prizes here!***

[Ittermat]

The Answer: 

The teacher, who does not bow back, serves to counterbalance the fact that each child is not required to bow to his or herself. There are 900 bows, and each child bows once for each other, so there are 30 children, as the square root of 900. As one third are boys, then there are 10 boys and 20 girls.