Greg asked me to post it myself. RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all mathematicians". Whether the latter is satisfied will be decided on a case-by-case basis. 3) If you have seen the problem before and remember the solution, you cannot participate in the solution to that problem. 4) You are allowed to use google, wolframalpha or any other resource. However, you are not allowed to search the question directly. So if the question was to solve an integral, you are allowed to obtain numerical answers from software, you are allowed to search for useful integration techniques, but you cannot type in the integral in wolframalpha to see its solution. CHALLENGE: You and a zombie are on a circle with 40,000 km circumference. You both cannot leave the circle, you can only move along the circle in both directions. The zombie will always move towards you at a constant speed of 4 km/h - at every moment it takes the direction where you are less than 20000 km away. If it reaches you, you die. During the day (16 hours), you can move at a maximal speed of v (larger than 4 km/h). If you get very close to the zombie during the day, you can see it and turn around to avoid it. During the night (8 hours), you have to sleep and cannot move. The zombie does not sleep. You start in the morning directly after waking up. The zombie starts at an unknown location along the ring. What is the minimal speed v to make sure you can stay safe forever, and how do you do that? Solved by jbriggs444 At this minimal speed, can you guarantee to get a bit of rest during the day eventually? Solved by jbriggs444 Can you guarantee to find the zombie?