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B4

Part of 2022 Putnam

Problems(1)

2022 Putnam B4

Source:

12/4/2022
Find all integers nn with n≥4n \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},…,{xn−2,xn−1,xn},{xn−1,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.
PutnamPutnam 2022