The percentage of boys in a Math circle, rounded to an integer is equal to 51%. The percentage of girls in this Math circle, rounded to an integer is equal to 49%. What is the minimal possible number of participants in the circle? (Source: "Formula of unity" contest, 2020 qualification rounds, R7, problem 2 - https://www.formulo.org/en/olymp/2020-math-en/)
What is a principled way to tackle such a problem?
Here was my sketch of solution: It is easy to see 51 - 49 is a solution, although not minimal.
Assuming the girls percentage can be at least 48.501 and boys percentage 51.499, and that the difference between the two is at least 1 -- I could guess the solution is somewhere around 33 children in the class. Then, 35 (17 + 18) is the smallest solution.