You are given two boxes: one box filled with mason jars of different sizes, and another box filled with corresponding screw top lids. You can test whether a given jar and lid are a match, from which1 you learn whether the jar is too large, too small, or an exact match for the lid. The differences insize between pairs of jars or lids are too small to see by eye, so you cannot compare the sizes oftwo jars or two lids directly. You are to match each jar to each lid, with the assumption that notwo jars or two lids are of the same size, and that every jar in one box has a corresponding lid inthe other box. Give a randomized O(nlogn) expected time algorithm for this problem.

Carlos, an algebra teacher, is creating a series of powerpoint presentations to use during class lectures. after writing, formatting, and stylizing the first presentation, he would like to begin writing the next presentation. he plans to insert all-new content, but he wants to have the same formatting and style as in the first one. what would be the most efficient way for carlos to begin creating the new presentation? going under the file tab and opening the first presentation, deleting all content from each page, and adding new content going under the file tab and clicking on new in the left pane, then choosing new from existing going under the design tab and clicking on themes, then selecting the theme that was used for the first template going under the design tab and opening the template that was created for the first presentation