Official material: complete proof · OBMEP solutions · collection of the year. The resolutions below follow the numbering of the official notebook. Open the test to follow the statements, alternatives and diagrams; The explanations here are copyright. Attempt each question before checking the answer. Template Questions Answers 1–5 E · B · A · E · C 6–10 E · A · B · E · C 11–15 C · B · B · E · D 16–20 B · D · E · C · C Question 1 — Pins The bottom left and bottom right sheets must keep their respective pins: no other holds them. It is also necessary to keep at least one pin from the top left sheet and one from the top right. So that leaves at least four of the ten. Choose, on these two upper sheets, pins that also secure the overlapping sheets in the middle. This choice supports the six sheets using four pins. We can remove $10-4=6$ — E.
Official material: complete proof · OBMEP solutions · collection of the year. The resolutions below follow the numbering of the official notebook. Open the test to follow the statements, alternatives and diagrams; The explanations here are copyright. Attempt each question before checking the answer. Question 1 — Cards and multiples a) One possibility is $6,2,4,8,1,9,3$. Checking the pairs, we have divisibility in all of them: 6 by 2, 4 by 2, 8 by 4, 8 by 1, 9 by 1 and 9 by 3.