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The Guts round is an 80-minute team event with 36 short-answer questions on an assortment of subjects, divided into 12 groups of 3 (in November) or 9 groups of 4 (in February). The problems' difficulty and point values increase with each subsequent set, culminating in the final set of estimation problems, typically worth 20 points each.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For example, if s=2, then π(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly π²/6. When s is a complex number—one that looks like a+bπ, using ...
The answer to the Harvard riddle is a simple "No." Forget all of the filler words meant to trick you in the beginning, and pay attention to the last line. It asks you directly if you can solve the ...
[1] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
Boolos provides the following clarifications: [1] a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a fair coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails ...
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...