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5664Why Monte Carlo Beats Trees In High DimensionWhy can Monte Carlo become more attractive than lattice methods as the number of risk factors grows?数理金融中等essay未尝试面试订阅5665Why Monte Carlo And Model Risk InteractWhy does a small Monte Carlo standard error not guarantee that the option price is actually reliable?数理金融中等essay未尝试面试订阅5666Balanced Parenthesis CountHow many ways can you arrange 5 left and 5 right parentheses in a row so that every prefix has at least as many left as right parentheses (i.e. the sequence is balanced)?脑筋急转弯中等数值题未尝试免费5667Hat-Check Derangement CountSix guests check distinct hats. The attendant returns the hats in a random order. In how many of the possible return orderings does no guest receive their own hat?脑筋急转弯中等数值题未尝试免费5668Secret-Santa No Self-Draw ProbabilityFive people draw names uniformly at random from a hat containing all five of their own names, one draw each, forming a random permutation. What is the probability that nobody draws their own name?脑筋急转弯中等数值题未尝试免费5669Five Gifts Four Children SurjectionFive distinct gifts are distributed to 4 distinct children so that every child receives at least one gift. In how many ways can this be done?脑筋急转弯中等数值题未尝试免费5670Coprime-to-2357 Count up to 1000How many integers from 1 to 1000 are divisible by none of 2, 3, 5, or 7?脑筋急转弯中等数值题未尝试免费5671At-Least-One Fixed Point CountOf the 120 permutations of the labels 1,2,3,4,5 , how many fix at least one label in its original position?脑筋急转弯中等数值题未尝试免费5672Trilingual Survey None-CountIn a group of 100 people, 50 speak French, 40 speak German, 35 speak Spanish; 18 speak both French and German, 15 both French and Spanish, 12 both German and Spanish, and 6 speak all three. How many speak none of these three languages?脑筋急转弯简单数值题未尝试免费5673Totient of 60 by SieveHow many integers in the range 1 to 60 are relatively prime to 60 (share no common factor greater than 1 with 60)?脑筋急转弯中等数值题未尝试免费5674At-Least-One Couple ReunitedFour married women and their four husbands are randomly paired into 4 man-woman dance pairs (a uniform random perfect matching). What is the probability that at least one woman is paired with her own husband?脑筋急转弯中等数值题未尝试免费5675Seating with Forbidden Own-ChairFour people, each with an assigned chair, are reseated so that no person sits in their own assigned chair, and additionally person 1 must not sit in chair 2. How many seatings are valid?脑筋急转弯困难数值题未尝试免费5676Seven Tasks Four Machines All BusySeven distinct tasks are each assigned to one of 4 distinct machines. In how many assignments is every machine used at least once?脑筋急转弯中等数值题未尝试免费5677Three-Pile Nim Winning MoveTwo players play standard Nim with three piles of sizes 3, 5, and 7. On a turn a player removes any positive number of stones from a single pile, and the player who takes the last stone wins. Does the first player win, and if so, give a winning first move (which pile and how many stones to remove).脑筋急转弯简单数值题未尝试免费5678Six Pirates and 100 CoinsSix pirates ranked 1 (most senior) to 6 must divide 100 gold coins. Starting with the most senior, the proposer suggests an allocation; all living pirates (including the proposer) vote. If at least half vote yes the plan passes; otherwise the proposer is thrown overboard and the next most senior proposes. Pirates are perfectly rational and value, in order: survival, then maximizing their own coins, then (as a tiebreaker) seeing others thrown overboard. How many coins does the most senior pirate keep?脑筋急转弯中等数值题未尝试免费5679Race to the Last of 100A single pile holds 100 stones. Players alternate removing between 1 and 7 stones (inclusive). The player who takes the last stone wins. Does the first player win, and if so how many stones should they remove on the first move?脑筋急转弯简单数值题未尝试免费5680First to Say Twenty-OneTwo players build a running total starting at 0. On each turn a player adds 1, 2, or 3 to the total. The player who makes the total reach exactly 21 wins. Does the first player win, and if so what number should they add on the very first move?脑筋急转弯简单数值题未尝试免费5681Misere Nim of SingletonsFive piles each contain exactly 1 stone. Players alternate removing one or more stones from a single pile; here the player forced to take the LAST stone LOSES (misere play). Under optimal play, does the first player win or lose?脑筋急转弯简单brainteaser未尝试免费5682Queen on the Quarter-BoardTwo piles hold 3 and 5 tokens. On a turn a player either removes any positive number from one pile, or removes the SAME positive number from both piles. The player taking the last token (emptying both piles) wins. With the position at (3, 5), does the player to move win or lose under optimal play?脑筋急转弯中等brainteaser未尝试免费5683Sum of Two Take-1-or-2 GamesTwo independent piles are in play, of sizes 4 and 7. On a turn a player picks ONE pile and removes 1 or 2 stones from it. The player who takes the last stone overall (leaving both piles empty) wins. Under optimal play, does the first player win or lose?脑筋急转弯中等brainteaser未尝试免费