Question 1
Several children are in a room with 1000 sweets in a bag. In some order, each child divides the current number of sweets by the current number of children in the room, rounds if necessary, takes that many sweets and leaves. Boys always round up and girls always round down. Prove that the total number of sweets taken by the boys is independent of the order. (4 points)
Neutral editorial illustration.
Practice scoring adds all whole-question scores (maximum 53). Official ITOT scoring adds only the three highest whole-question scores (maximum 31), after summing subparts within each question. The importer does not enforce best-three scoring. Duration: 300 minutes from historical organizer general rules, not an individually printed duration on this paper.
Neutral editorial illustration.
Practice scoring adds all whole-question scores (maximum 53). Official ITOT scoring adds only the three highest whole-question scores (maximum 31), after summing subparts within each question. The importer does not enforce best-three scoring. Duration: 300 minutes from historical organizer general rules, not an individually printed duration on this paper.