BG-MO 2023 Problem 5 For every positive integer nnn determine the least possible value of the expression ∣x1∣+∣x1−x2∣+∣x1+x2−x3∣+⋯+∣x1+x2+⋯+xn−1−xn∣|x_{1}|+|x_{1}-x_{2}|+|x_{1}+x_{2}-x_{3}|+\dots +|x_{1}+x_{2}+\dots +x_{n-1}-x_{n}|∣x1∣+∣x1−x2∣+∣x1+x2−x3∣+⋯+∣x1+x2+⋯+xn−1−xn∣ given that x1,x2,…,xnx_{1}, x_{2}, \dots , x_{n}x1,x2,…,xn are real numbers satisfying ∣x1∣+∣x2∣+⋯+∣xn∣=1|x_{1}|+|x_{2}|+\dots+|x_{n}| = 1∣x1∣+∣x2∣+⋯+∣xn∣=1 . Dataset text AI-MO AoPS. Quoted with source. Solutions No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label. Add a solution Similar problems These problems have the most words in common with this statement. KZ-MO 2003 Problem 1IL-GILLIS 2013 Problem 6CMO 1988 Problem 4AIME 1988 Problem 4Putnam 1986 A6 PreviousProblem 4 NextProblem 6 Locator bg-mo/2023/p5 · Tag DHC01PGMWQ · Edit this page on GitHub · Keys: j next, k previous