Question 1
SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
Given $S=\{1,2,\ldots,10\}$, a family $F$ of subsets of $S$ is intersecting if any two members $A,B$ have a nonempty intersection $A\cap B$. What is the maximum size of $F$?
Enter the exact number only; fractions are allowed.
Given $S=\{1,2,\ldots,10\}$, a family $F$ of subsets of $S$ is intersecting if any two members $A,B$ have a nonempty intersection $A\cap B$. What is the maximum size of $F$?
Enter the exact number only; fractions are allowed.