Asked two brain-teasers: 1) You have two strings which are identical. If you light a string from one end, it will burn in exactly one hour. However, the rate of burning may vary along the string, so it may burn faster, then slower, then faster etc. How do you measure exactly 45 minutes using both strings? 2) You have a one meter ruler. We will drop 200 ants on to the ruler, each ant falling at a location along the ruler which is uniformly distrubuted. When an ant falls, it goes left or right with equal probability. When two ants bump into each other they reverse directions. Each ant moves along the string at a speed of 1 meter per minute. How long will it take for all the ants to fall off the ruler?

two phone screens. some interviewers were nice and others were more strict, lots of interesting math and research discussed. got asked a flurry of technicals, ramping up in difficulty each time, and even some open ended questions where they explicitly said there is no interview-tractable solution and just wanted to hear my ideas for an approach