Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2019 USAJMO Problems/Problem 5

Revision as of 18:11, 19 April 2019 by Kevinmathz (talk | contribs) (Created page with "Let <math>n</math> be a nonnegative integer. Determine the number of ways that one can choose <math>(n+1)^2</math> sets <math>S_{i,j}\subseteq\{1,2,\ldots,2n\}</math>, for int...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Let $n$ be a nonnegative integer. Determine the number of ways that one can choose $(n+1)^2$ sets $S_{i,j}\subseteq\{1,2,\ldots,2n\}$, for integers $i,j$ with $0\leq i,j\leq n$, such that: [list] [*] for all $0\leq i,j\leq n$, the set $S_{i,j}$ has $i+j$ elements; and [*] $S_{i,j}\subseteq S_{k,l}$ whenever $0\leq i\leq k\leq n$ and $0\leq j\leq l\leq n$. [/list]

[i]Proposed by Ricky Liu[/i]

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2019_USAJMO_Problems/Problem_5&oldid=105370"