A psychopathic serial killer brings you into a room with 50 wooden coffins. The top cover of each coffin is painted with the portrait of one of your closest friends, except one coffin which has your picture on it. You cannot detect what's actually inside any coffin until you open it. In each of these coffins, exactly one prisoner is trapped (a random person you know, potentially but not necessarily the same as the one shown on the cover), except for one coffin in which there lies a mirror facing you. If you open that coffin, all of your remaining friends will be spared and everyone still alive be allowed to leave. Whenever you open a coffin, a trap will be activated that immediately kills anyone lying within (unless it's a mirror, of course) and releases a fixed amount of toxic gas each time. You can only open up to 25 coffins before the buildup of poison suffocates you to death. Can you devise a way to rescue at least half of your friends with better than a 50% chance? Is it even doable?Optional clarifications:Also, you should not attempt anything heroic or violent like attacking your captor (he is armed and constantly watching you). The kidnapper does not remember where he placed each victim, so you won't get any information out of him no matter how you ask. He is strict and will not allow you to do anything besides prying open coffins. No communication or reception of external assistance from the outside world is feasible or permitted. All coffins are opaque and identical, except that each coffin is painted with a unique image, and each coffin conceals a something different (yours contains a mirror, reflecting "you"). The placements were made purely randomly; that is, each coffin is equally likely to be enclosing any of the 50 possibilities. Dead corpses cannot be revived, and you will not have a chance to talk with them. You have 24 hours, but the effect of the poison does not wear off over time. However immoral, the gamemaster is honest at keeping his word, and will release everyone remaining by the end of the game if you win. If even after opening up 25 coffins you still cannot see your shameful self in the mirror, he will think you're pathetic and decide to bomb the entire place suicide-style.1. Instead of seeking any satisfactory solution whose success rate exceeds 50%, try to find the optimal. It is guaranteed to exist, and in fact, the likelihood of survival is greater than 60%.2. Assigning numbers from 1 to 50 as labels might be a promising idea. It does not matter whether they are fleshed people stuck in wooden containers or slips of paper covered by cardboard boxes. The gothic-scifi-horror atmosphere is not important.3. Think about the information you're provided. You have two types of clues: the portrait on each coffin which has already been revealed, and the encapsulated entity which you could uncover. How can you incorporate this information into your strategy?4. Which coffin do you want to open first?5. This puzzle can be compared to an iterated version of the the Monty Hall conditional probability problem, with one goat and one car each hidden behind a door, with a third door held open. After you open the first coffin and see what's there, which coffin do you open next?