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143No Consecutive Heads in Six FlipsYou flip 6 fair coins in sequence. What is the probability that no two consecutive coins land heads?概率中等数值题未尝试免费576Discrete Signal Stop Rule 1You may inspect up to 2 independent signals, each uniformly distributed on 1,...,7 . After seeing a signal, you may lock it in and stop. Rejecting a signal and continuing costs 1 point(s). If you reach the last draw, you must take it. What first-round acceptance threshold is optimal, and what is the expected net score?概率简单数值题未尝试免费586Weighted Offer Stop Rule 1You may inspect up to 2 independent offers. Each offer takes values 1 with probability 1/4, 4 with probability 1/2, 9 with probability 1/4. Rejecting an offer and continuing costs 1 point(s), and if you reach the last draw you must accept it. What first-round acceptance threshold is optimal, and what is the resulting expected net payoff?概率简单数值题未尝试免费590Weighted Offer Stop Rule 5You may inspect up to 3 independent offers. Each offer takes values 0 with probability 1/4, 4 with probability 1/4, 7 with probability 1/4, 12 with probability 1/4. Rejecting an offer and continuing costs 1 point(s), and if you reach the last draw you must accept it. What first-round acceptance threshold is optimal, and what is the resulting expected net payoff?概率困难derivation未尝试免费596Continuation Value Calibration 1A trader may inspect up to 4 independent candidate fills with support [2, 5, 9] and probabilities ['1/3', '1/3', '1/3']. Rejecting a fill and continuing costs 1. What first observation becomes just good enough to accept, and what is the overall optimal expected net value?概率简单数值题未尝试免费597Continuation Value Calibration 2A trader may inspect up to 3 independent candidate fills with support [1, 4, 8, 11] and probabilities ['1/4', '1/4', '1/4', '1/4']. Rejecting a fill and continuing costs 1. What first observation becomes just good enough to accept, and what is the overall optimal expected net value?概率简单数值题未尝试免费683Venue-Session Tag Collision 3Each quote is classified by one of 3 venues and one of 6 session buckets. How many quotes guarantee that two quotes share the same ordered pair of tags?脑筋急转弯中等brainteaser未尝试免费684Parity-and-Desk Match 4On a floor with 5 desks, each ticket also has one of 2 parity labels. How many tickets guarantee that two tickets share both the same desk and the same parity label?脑筋急转弯中等brainteaser未尝试面试订阅694Column Pattern Coincidence 4Nine binary columns each record a 3-day sign pattern. Show that two columns have exactly the same pattern.脑筋急转弯困难brainteaser未尝试面试订阅731Positive Composition Count 1How many ordered compositions of 10 into 4 positive parts are there?脑筋急转弯中等brainteaser未尝试免费741Committee-with-Chair Count 1From 8 labeled people, how many ordered pairs (committee, chair) are there where the committee has size 3 and the chair is a member of the committee?脑筋急转弯简单数值题未尝试免费748Two-Stage Allocation Count 3How many ways can 9 identical tokens be split into 3 positive piles and then choose one token from the largest-index nonempty pile to mark?脑筋急转弯中等brainteaser未尝试免费749Subset-Path Correspondence 4How many lattice paths from (0,0) to (4,6) are there?脑筋急转弯中等数值题未尝试免费753Market-State Logic Grid 3Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'The market is bear.' C says: 'At least one of B and C is lying.' Determine the market state and the type of each analyst.脑筋急转弯中等brainteaser未尝试免费755Market-State Logic Grid 5Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'Exactly one of us is truthful.' C says: 'B and C are the same type.' Determine the market state and the type of each analyst.脑筋急转弯困难brainteaser未尝试免费757Market-State Logic Grid 7Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'Exactly one of us is truthful.' C says: 'At least one of B and C is lying.' Determine the market state and the type of each analyst.脑筋急转弯中等brainteaser未尝试免费758Market-State Logic Grid 8Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'Exactly one of us is truthful.' C says: 'The number of truthful analysts is odd.' Determine the market state and the type of each analyst.脑筋急转弯中等brainteaser未尝试免费759Market-State Logic Grid 9Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'Exactly two of us are truthful.' C says: 'The market is bull.' Determine the market state and the type of each analyst.脑筋急转弯中等brainteaser未尝试免费760Market-State Logic Grid 10Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'Exactly two of us are truthful.' C says: 'At least one of B and C is lying.' Determine the market state and the type of each analyst.脑筋急转弯困难brainteaser未尝试面试订阅764Market-State Logic Grid 14Three analysts A, B, and C are each either truthful (always tell the truth) or lying (always make false statements). The hidden market state is either bull or bear. A says: 'The market is bull.' B says: 'A and C are different types.' C says: 'A and B are both truthful.' Determine the market state and the type of each analyst.脑筋急转弯困难brainteaser未尝试免费