16
Part of 2018 Online Math Open Problems
Problems(2)
2017-2018 Spring OMO Problem 16
Source:
4/3/2018
In a rectangular grid of cells, of the cells are colored black. What is the smallest positive integer such that there must exist a rectangle, with sides parallel to the edges of the grid, that has its four vertices at the center of distinct black cells?Proposed by James Lin
2018-2019 Fall OMO Problem 16
Source:
11/7/2018
Jay has a grid of lights, all of which are initially off. Each of the rows and columns has a switch that toggles all the lights in that row and column, respectively, i.e. it switches lights that are on to off and lights that are off to on. Jay toggles each of the rows and columns exactly once, such that after each toggle he waits for one minute before the next toggle. Each light uses no energy while off and 1 kiloJoule of energy per minute while on. To express his creativity, Jay chooses to toggle the rows and columns in a random order. Compute the expected value of the total amount of energy in kiloJoules which has been expended by all the lights after all toggles.Proposed by James Lin