MathDB
Wot n' Subset Formation

Source: 2017 AIME I #12

March 8, 2017
2017 AIME IcombinatoricsSetsrecursionAIMEAIME IAMC

Problem Statement

Call a set SS product-free if there do not exist a,b,cāˆˆSa, b, c \in S (not necessarily distinct) such that ab=ca b = c. For example, the empty set and the set {16,20}\{16, 20\} are product-free, whereas the sets {4,16}\{4, 16\} and {2,8,16}\{2, 8, 16\} are not product-free. Find the number of product-free subsets of the set {1,2,3,4,5,6,7,8,9,10}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}.
Back to ProblemsView on AoPS