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3861Why Basis Risk Makes a Cash-Futures Hedge ImperfectWhy can a cash-futures hedge still leave risk even if the futures notional matches the cash position perfectly?金融与交易中等essay未尝试面试订阅3862Why Basis Tends to Converge Near ExpiryWhy does basis often shrink as a futures contract approaches expiry?金融与交易中等essay未尝试面试订阅3863Why Basis Can Be Negative in ContangoWhy does the cash basis S-F become negative in contango markets?金融与交易中等essay未尝试面试订阅3864Why Basis Can Be Positive in BackwardationWhy does the cash basis S-F become positive in backwardation?金融与交易中等essay未尝试面试订阅3865Why Traders Monitor Basis Separately from Outright PriceWhy is basis worth monitoring as its own state variable rather than only watching spot and futures separately?金融与交易中等essay未尝试面试订阅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5698Twelve Coins, Unknown DirectionYou have 12 coins that look identical. Exactly one is counterfeit and has a different weight from the rest, but you do NOT know whether it is heavier or lighter. Using only a two-pan balance scale (each weighing reports left-heavy, right-heavy, or balanced), what is the minimum number of weighings that guarantees you both identify the counterfeit AND determine whether it is heavy or light? Weighings may be chosen adaptively.脑筋急转弯中等brainteaser未尝试免费5700Ten Hats in a Line10 players stand in a line. Each wears a red or blue hat, assigned independently by a fair coin. Each player sees all hats in FRONT of them but not their own nor those behind. Starting from the back of the line, each player in turn announces a single guess of their own hat color, heard by everyone. They agree on a strategy beforehand (no communication after hats are placed except the public guesses). Using the optimal parity strategy, how many of the 10 players are GUARANTEED to guess correctly regardless of the hat assignment?脑筋急转弯中等brainteaser未尝试免费5702One Poisoned Bottle, Binary TestersYou have 1000 bottles of wine, exactly one of which is poisoned. A tester who drinks any amount containing the poison dies after exactly the same fixed delay, and you can have each tester sip from any combination of bottles simultaneously in a single round (results observed after the delay, before the celebration). If you only get ONE round of testing, what is the minimum number of testers needed to guarantee identifying the poisoned bottle?脑筋急转弯中等brainteaser未尝试免费5705Prisoners and the Lightbulb Counter100 prisoners take turns, one at a time in an arbitrary order chosen by a warden, entering a room with a single lightbulb (initially OFF). Each visiting prisoner may toggle the bulb and observe its state, but cannot otherwise communicate. At any point any prisoner may declare 'every prisoner has now visited at least once'; they win only if the declaration is true. They strategize beforehand. In the standard single-counter strategy, exactly one designated counter increments a tally when he finds the bulb ON (then switches it OFF), and every other prisoner switches the bulb ON the FIRST time they find it OFF (and never again). What total count must the counter reach before he can safely declare everyone has visited?脑筋急转弯困难brainteaser未尝试面试订阅5706How Many Coins in Three Weighings (Known Heavy)Among a pile of identical-looking coins exactly one is counterfeit and is known to be HEAVIER than the others. With a two-pan balance scale (each weighing returns left-heavy, right-heavy, or balanced) and exactly 3 weighings allowed, what is the LARGEST number of coins for which you can always guarantee identifying the heavy one? Weighings may be adaptive.脑筋急转弯简单brainteaser未尝试免费5707100 Prisoners and 100 Boxes100 prisoners are numbered 1 to 100. In a room, 100 boxes each contain one slip with a distinct number 1 to 100, placed by a uniformly random permutation. Each prisoner enters alone, may open at most 50 boxes, must find the slip bearing his own number, then leaves without communicating or altering anything. All 100 must succeed for the group to win. Using the optimal strategy (each prisoner opens the box with his number, then the box whose number matches the slip just found, following the permutation cycle), the win probability equals 1 minus the sum of 1/k for k from 51 to 100. To the nearest whole percent, what is this winning probability?脑筋急转弯困难brainteaser未尝试面试订阅5708Reference Coin Boosts CapacityExactly one coin among a pile is counterfeit, with weight different from the genuine ones, but you do NOT know whether it is heavier or lighter. You also have ONE extra coin that is guaranteed genuine, which you may place on the scale freely. Using a two-pan balance (each weighing returns left-heavy, right-heavy, or balanced) with exactly 3 weighings, what is the LARGEST number of suspect coins for which you can always both identify the fake and determine its direction? Weighings may be adaptive.脑筋急转弯困难brainteaser未尝试面试订阅5710Digital Scale, Subset WeighingYou have 8 coins; exactly one is counterfeit and is KNOWN to be lighter than each genuine coin (all genuine coins weigh the same). Instead of a balance, you have a DIGITAL scale that reports the exact total weight of any subset of coins you place on it. Each placement-and-reading counts as one weighing. What is the minimum number of weighings that always identifies the light coin, and can a single weighing ever suffice? Give the minimum number of weighings.脑筋急转弯简单brainteaser未尝试免费5711Seven Heads, Three Colors7 people sit in a circle, each wearing a hat colored red, green, or blue (assigned independently and arbitrarily). Everyone sees all hats except their own. They must all SIMULTANEOUSLY write down a guess of their own hat color (no information exchange after seeing the hats). They agree on a strategy beforehand. Using the optimal modular-sum strategy, what is the maximum number of the 7 people they can GUARANTEE will guess correctly, no matter how the hats are assigned?脑筋急转弯中等brainteaser未尝试免费5712Four Glasses on a Spinning TableFour glasses sit at the corners of a square rotating table, each independently up or down (initial configuration unknown). On each move a blindfolded robot may reach into any TWO of the four positions, feel their orientations, and flip either, both, or neither. After each move the table is spun by an adversary to an unknown rotation, so the robot never knows absolute positions, only relative ones (it can choose 'two adjacent' or 'two diagonal'). A bell rings the instant all four glasses match (all up or all down). What is the minimum number of moves that GUARANTEES the bell rings in the worst case?脑筋急转弯困难brainteaser未尝试面试订阅5718The Carry-One Ferry with Incompatible CargoA trader must ferry three items — a fox, a goose, and a sack of beans — across a river in a small boat that can carry the trader plus at most one item per trip. If left together unattended, the fox eats the goose, and the goose eats the beans (the fox ignores the beans). The trader rows every trip. What is the minimum number of one-way crossings needed to get all three items safely to the far bank?脑筋急转弯简单brainteaser未尝试免费5722Timing Fifteen Minutes with Two HourglassesYou have a 7-minute hourglass and an 11-minute hourglass, and you must time a process that takes exactly 15 minutes. You may start the process only at the moment you begin timing, and you may flip either hourglass whenever it runs out (or at any time). Using only these two hourglasses, what is the least total elapsed time in which you can mark off exactly a 15-minute interval starting from time zero?脑筋急转弯困难brainteaser未尝试面试订阅