Cla­ri­fic­a­tions to the problems

Dear par­ti­cipants! We have received many cla­ri­fy­ing ques­tions regard­ing the con­di­tions of the problems.
Many of them are answered in the con­di­tions, but there are sev­er­al cases where the con­di­tions are for­mu­lated impre­cisely or ambigu­ously. There­fore, we provide comments.
In the fol­low­ing text, the prob­lem num­bers are indic­ated as fol­lows: «8.1» means «prob­lem #1 for the grade R8».

6.7, 7.5, 8.5. Sofia takes one or more pho­tos FROM THE TOP of any pile.
9.1 (about the king of the class): it is known that there were at least four tests. Phrase (с) means that STRICTLY LESS par­ti­cipants dropped out in the first test than in any oth­er test.
5.5. Each boy knows EXACTLY four girls.
7.6, 8.6, 9.6. Only the inter­ac­tion BETWEEN the two selec­ted chil­dren is observed — they can still pass cheat sheets to the REST of their acquaintances.
9.7, 10.7. It is neces­sary that no sub­set of rect­angles form a rect­angle IN THE PLACE where they are ini­tially loc­ated. That is, for example, if two 1×1 squares are found some­where far from each oth­er, their uni­on DOES NOT FORM a rectangle.