Art of Problem Solving

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  • 15:12, 6 November 2025 Jonathanmo talk contribs created page 2025 AMC 12A Problems/Problem 5 (Created page with "==Problem 13== In the figure below, the outside square contains infinitely many squares, each of them with the same center and sides parallel to the outside square. The ratio of the side length of a square to the side length of the next inner square is <imath>k</imath>, where <imath>0 < k < 1.</imath> The spaces between squares are alternately shaded as shown in the figure (which is not necessarily drawn to scale). <asy> unitsize(1cm); int n = 25; real s...")
  • 15:07, 6 November 2025 Jonathanmo talk contribs created page 2025 AMC 12A Problems/Problem 15 (Created page with "==Problem 21== A set of numbers is called <imath>sum</imath>-<imath>free</imath> if whenever <imath>x</imath> and <imath>y</imath> are (not necessarily distinct) elements of the set, <imath>x+y</imath> is not an element of the set. For example, <imath>\{1,4,6\}</imath> and the empty set are sum-free, but <imath>\{2,4,5\}</imath> is not. What is the greatest possible number of elements in a sum-free subset of <imath>\{1,2,3,...,20\}</imath>? <imath>\textbf{(A) } 8 \qquad...")
  • 19:56, 29 March 2025 User account Jonathanmo talk contribs was created automatically