Question 1
Twelve cards numbered 1 through 12 are dealt to four wizards $A,B,C,D$, three each. Each sees only their own cards. They speak in order: A: “I have card 8.” B: “All three of my numbers are prime.” C: “I have three composite numbers with a common prime divisor.” D: “Now I know everyone's cards.” All statements are true. Which cards does A have? (5 points)
Neutral editorial illustration.
Practice scoring adds all whole-question scores (maximum 57). 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 57). 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.