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5728Tower of Hanoi with Five DisksFive disks of distinct sizes are stacked on the first of three pegs, largest at the bottom and smallest on top. You move disks one at a time from the top of any peg to the top of another peg, and a disk may never be placed on top of a smaller disk. What is the minimum number of single-disk moves needed to transfer the entire stack to the third peg?脑筋急转弯中等brainteaser未尝试免费5729One Hundred LockersThere are 100 lockers, numbered 1 to 100, all initially closed. A student makes 100 passes along the row. On pass k (for k from 1 to 100) the student toggles every locker whose number is a multiple of k — opening it if closed, closing it if open. After all 100 passes are complete, how many lockers are left open?脑筋急转弯中等brainteaser未尝试免费5730Splitting Eight Units with Three JugsYou have three unmarked jugs with capacities 8, 5, and 3 units. The 8-unit jug starts completely full and the other two are empty; there is no other water source and no drain (water may only be poured between jugs). A pour transfers from one jug to another until the source is empty or the destination is full, and counts as one operation. What is the minimum number of pours needed to end with exactly 4 units in the 8-jug and 4 units in the 5-jug?脑筋急转弯困难brainteaser未尝试面试订阅5731Paying with a Gold ChainA traveler must pay an innkeeper one gold link per day for seven days, using a chain of 7 identical links. The innkeeper insists on holding exactly the right number of links each day, but is willing to give change from links already paid (so the traveler can hand over a larger piece and take back smaller ones). The traveler may cut some links open to break the chain into pieces. What is the minimum number of links that must be cut so that a correct payment can be made every day for all seven days?脑筋急转弯困难brainteaser未尝试面试订阅5732Scheduling Jobs Before Their DeadlinesFive jobs each take exactly one hour of machine time on a single machine, which can run one job per hour starting at hour 1. Each job earns its profit only if it is completed by its deadline (the hour by which it must finish); a job finished after its deadline, or not run at all, earns nothing. The jobs are: A (deadline 2, profit 100), B (deadline 1, profit 19), C (deadline 2, profit 27), D (deadline 1, profit 25), E (deadline 3, profit 15). You choose which jobs to run and in what order. What is the maximum total profit obtainable?脑筋急转弯困难brainteaser未尝试面试订阅5733Minimum Boats to Carry EveryoneFive people weighing 50, 50, 70, 80, and 90 kilograms must cross a lake. Each boat can carry at most two people and at most 140 kilograms total. Assume you have as many boats as you like, all departing together, so you only care about how many boats are required (not return trips). What is the minimum number of boats needed so that everyone can cross?脑筋急转弯中等brainteaser未尝试免费5894Kelly Fraction at General Net OddsA favorable bet pays net odds b to 1: staking an amount, you gain b times the stake with probability p and lose the stake with probability 1-p. Betting a fraction f of wealth each round, derive the growth-optimal fraction f * in terms of b and p.概率简单derivation未尝试免费6014Quadrupling the SampleYour current backtest detects a minimum edge of 6 bp at the desired power. You extend the sample so the number of observations is multiplied by 4, keeping sigma, alpha, and target power fixed. Because the minimum detectable effect scales as 1/sqrt(n), what is the new minimum detectable edge, in basis points?统计简单数值题未尝试免费