MathDB

Counting Subsets

Source: 2023 AIME I #11

February 8, 2023

AMCAIMEAIME I

Problem Statement

Find the number of subsets of

{1,2,3,...,10}

that contain exactly one pair of consecutive integers. Examples of such subsets are

{1,2,5}

and

{1,3,6,7,10}