75th Romanian Mathematical Olympiad

Initially, the students are grouped $(G,B,B,B),(G,B,B,B),(G,B,B,B),\dots ,(G,B,B,B)$. When two girls and a boy are missing, the situation (replacing a boy, if the missing boy is not in the same team as one of the missing girls) becomes: $(G,B,B),(G,B,B,B),(G,B,B,B),\dots ,(G,B,B,B)$. Since each new group has one girl, the $2+3$ boys from the incomplete initial groups must be regrouped so that we get groups with 4 boys and one girl – one in each initial group. This means that now we have five groups, therefore now there are $5\cdot 4=20$ boys and 5 girls. Hence, the robotics workshop has $20+1=21$ boys and $5+2=7$ girls, for a total of 28 registered students.