MathDB
2022 Putnam B4

Source:

December 4, 2022
PutnamPutnam 2022

Problem Statement

Find all integers nn with n4n \geq 4 for which there exists a sequence of distinct real numbers x1,,xnx_1, \ldots, x_n such that each of the sets {x1,x2,x3},{x2,x3,x4},,{xn2,xn1,xn},{xn1,xn,x1}, and {xn,x1,x2}\{x_1, x_2, x_3\}, \{x_2, x_3, x_4\},\ldots,\{x_{n-2}, x_{n-1}, x_n\}, \{x_{n-1}, x_n, x_1\},\text{ and } \{x_n, x_1, x_2\} forms a 3-term arithmetic progression when arranged in increasing order.