Task: Question Answering
Input (English): Context_1 : Pancake sorting is the colloquial term for the mathematical problem of sorting a disordered stack of pancakes in order of size when a spatula can be inserted at any point in the stack and used to flip all pancakes above it. A "pancake number" is the minimum number of flips required for a given number of pancakes. In this form, the problem was first discussed by American geometer Jacob E. Goodman. It is a variation of the sorting problem in which the only allowed operation is to reverse the elements of some "prefix" of the sequence. Unlike a traditional sorting algorithm, which attempts to sort with the fewest comparisons possible, the goal is to sort the sequence in as few reversals as possible. A variant of the problem is concerned with "burnt" pancakes, where each pancake has a burnt side and all pancakes must, in addition, end up with the burnt side on bottom. Context_2 : A problem statement is a short description of the issues that need to be addressed by a problem solving team and should be presented to them (or created by them) before they try to solve a problem. On the other hand, "a statement of the problem" is a claim of one or two sentences in length that outlines the problem addressed by a study. The statement of the problem should briefly address the question: What is the problem that the research will address? Context_3 : In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group "G" is the algorithmic problem of deciding whether two words in the generators represent the same element. More precisely, if "A" is a finite set of generators for "G" then the word problem is the membership problem for the formal language of all words in "A" and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on "A" to the group "G". If "B" is another finite generating set for "G", then the word problem over the generating set "B" is equivalent to the word problem over the generating set "A". Thus one can speak unambiguously of the decidability of the word problem for the finitely generated group "G". Context_4 : In probability and game theory, the Waldegrave problem refers to a problem first described in the second edition of Montmort`s "Essay d'analyse sur les jeux de hazard". This problem is remarkable in that it is the first appearance to a mixed strategy solution in game theory. Montmort originally called Waldegrave’s Problem the "Problème de la Poulle" or the Problem of the Pool. He provides a minimax mixed strategy solution to a two-person version of the card game le Her. It was Isaac Todhunter who called it Waldegrave’s Problem. The general description of the problem is as follows: Suppose there are n+1 players with each player putting one unit into the pot or pool. The first two players play each other and the winner plays the third player. The loser of each game puts one unit into the pot. Play continues in like fashion through all the players until one of the players has beaten all the others in succession. The original problem, stated in a letter dated 10 April, 1711, from Montmort to Nicholas Bernoulli is for n = 2 and is attributed to "M. de Waldegrave". The problem, according to Montmort, is to find the expectation of each player and the probability that the pool will be won within a specified number of games. Context_5 : In geometric probability, the problem of Buffon's noodle is a variation on the well-known problem of Buffon's needle, named after Georges-Louis Leclerc, Comte de Buffon who lived in the 18th century. That problem solved by Buffon was the earliest geometric probability problem to be solved. Context_6 : The Tunnel Problem is a philosophical thought experiment first introduced by Jason Millar. It is a variation on the classic Trolley Problem, a thought experiment introduced in the 1960s, and much discussed ever since. The tunnel problem is intended to draw one's attention to a specific issue in design/engineering ethics, and was first presented as follows: Context_7 : In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities "E", and two expressions "x" and "y", is it possible to transform "x" into "y" using the identities in "E" as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable. Context_8 : The trolley problem is a thought experiment in ethics. The general form of the problem is this:There is a runaway trolley barreling down the railway tracks. Ahead, on the tracks, there are five people tied up and unable to move. The trolley is headed straight for them. You are standing some distance off in the train yard, next to a lever. If you pull this lever, the trolley will switch to a different set of tracks. However, you notice that there is one person on the side track. You have two options: Context_9 : Thermotunnel cooling is similar to thermionic emission cooling in that fast moving electrons carry heat across a gap but cannot return due to a voltage difference. The problem with using thermal electrons to carry heat is the fact that, due to the high work function of metals, which are the only practical emitters, the lowest cooling temperate is around 600 °C - clearly not useful except in the most unusual applications. Thermotunnel cooling avoids this problem by making the gap narrow enough that electrons can tunnel across the gap, carrying the heat with them. The problem with this approach has been getting two surfaces near enough that they can tunnel over a large area, yet not touch at any point, which would short the device out preventing it from doing any useful cooling. Context_10 : In computing, the Two Generals Problem is a thought experiment meant to illustrate the pitfalls and design challenges of attempting to coordinate an action by communicating over an unreliable link. It is related to the more general Byzantine Generals Problem (though published long before that later generalization) and appears often in introductory classes about computer networking (particularly with regard to the Transmission Control Protocol where it shows that TCP can't guarantee state consistency between endpoints and why), though it applies to any type of two party communication where failures of communication are possible. A key concept in epistemic logic, this problem highlights the importance of common knowledge. Some authors also refer to this as the Two Generals Paradox, the Two Armies Problem, or the Coordinated Attack Problem. The Two Generals Problem was the first computer communication problem to be proved to be unsolvable. An important consequence of this proof is that generalizations like the Byzantine Generals problem are also unsolvable in the face of arbitrary communication failures, thus providing a base of realistic expectations for any distributed consistency protocols. fact_1 : The Tunnel Problem is a philosophical thought experiment first introduced by Jason Millar. fact_2 :  It is a variation on the classic Trolley Problem, a thought experiment introduced in the 1960s, and much discussed ever since. fact_3 : The trolley problem is a thought experiment in ethics. fact_4 :  You have two options: Question:  The Tunnel Problem is a variation on a problem in which you have two what?
Output (English): options