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3

Part of 2019 HMIC

Problems(1)

Four points at large distance

Source: HMIC 2019 Problem 3

4/28/2019
Do there exist four points Pi=(xi,yi)∈R2 (1≤i≤4)P_i = (x_i, y_i) \in \mathbb{R}^2\ (1\leq i \leq 4) on the plane such that:
[*] for all i=1,2,3,4i = 1,2,3,4, the inequality xi4+yi4≤xi3+yi3x_i^4 + y_i^4 \le x_i^3+ y_i^3 holds, and [*] for all i≠ji \neq j, the distance between PiP_i and PjP_j is greater than 11?
Pakawut Jiradilok
algebraHMIC