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5704Heaviest and Runner-UpYou have 8 coins of pairwise-distinct weights and a balance scale that compares two single coins and tells you which is heavier. What is the minimum number of pairwise weighings, in the worst case, needed to identify BOTH the heaviest coin and the second-heaviest coin? (This is the classic tournament problem.)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5709Two Light Fakes Among SixYou have 6 visually identical coins. Exactly TWO of them are counterfeit and each counterfeit weighs the same known-lighter amount (both fakes are equally light); the other four are genuine and equal. Using a two-pan balance scale (each weighing returns left-heavy, right-heavy, or balanced), what is the minimum number of weighings that guarantees identifying WHICH two coins are the light pair in the worst case? 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5713Two Eggs, One Hundred FloorsA building has 100 floors. There is a critical floor f such that an egg dropped from floor f or above breaks, and an egg dropped from any floor below f survives (f may be any of 1..100, or eggs never break, treated as f = 101). You have exactly 2 identical eggs; a broken egg cannot be reused, but an egg that survives a drop can be dropped again. What is the minimum number of drops that GUARANTEES determining f in the worst case? (Drops may be chosen adaptively.)脑筋急转弯中等brainteaser未尝试免费5714Twenty Questions With One LieAn adversary picks a secret integer from 1 to 16 inclusive. You ask yes/no questions chosen adaptively, but the adversary is allowed to answer FALSELY at most once during the whole game (it may also never lie). What is the minimum number of questions that GUARANTEES you can determine the secret number in the worst case?脑筋急转弯困难brainteaser未尝试面试订阅5715Bridge and Torch CrossingFour people must cross a rickety bridge at night. They have one torch, and the bridge holds at most two people at a time. Anyone on the bridge must carry the torch, so the torch must be walked back for the next group. The four people walk at different speeds, needing 1, 2, 5, and 10 minutes respectively to cross; when two cross together they move at the slower person's pace. What is the minimum total time for all four to get across?脑筋急转弯中等brainteaser未尝试免费5716Measuring Four Units with a 3-Jug and a 5-JugYou have an unlimited water supply, a 3-unit jug, and a 5-unit jug, both unmarked. The only operations allowed are: fill a jug completely from the supply, empty a jug onto the ground, or pour from one jug into the other until the source is empty or the destination is full. What is the minimum number of such operations needed to end with exactly 4 units of water in a jug?脑筋急转弯简单brainteaser未尝试免费5717Ferrying Guards and PrisonersThree guards and three prisoners must cross a river using a single boat that holds at most two people and cannot cross empty (someone must row it). At no time and on neither bank may prisoners outnumber the guards present there (if guards are present); if no guard is on a bank, any number of prisoners there is fine. Everyone can row. What is the minimum number of one-way boat trips needed to move all six across safely?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5719Two Eggs, One Hundred FloorsThere is a 100-floor building and two identical eggs. An egg breaks if dropped from floor h or above for some unknown threshold h (and survives any drop below h); a survived egg can be reused, a broken one cannot. You want to determine h with certainty. Drops are made one at a time and you choose each next floor adaptively. What is the minimum number of drops that guarantees you can identify h in the worst case?脑筋急转弯困难brainteaser未尝试面试订阅5720Sorting Pancakes by Spatula FlipsA stack of four pancakes has diameters, from top to bottom, 3,1,4,2 (all distinct). The only allowed move is to insert a spatula under any pancake and flip the entire block above it, reversing the order of that top prefix. You want the pancakes sorted with the largest on the bottom and the smallest on top (i.e. top-to-bottom 1,2,3,4). What is the minimum number of flips required?脑筋急转弯中等brainteaser未尝试免费5721Shortest Possible Project Completion TimeA project has six tasks with durations (in hours): A=3, B=2, C=4, D=1, E=5, F=2. The precedence constraints are: A must finish before C and D start; B must finish before D starts; C and D must both finish before E starts; D must finish before F starts. Any number of tasks may run in parallel as long as all their prerequisites are complete. Starting at time 0, what is the earliest time at which all six tasks are finished?脑筋急转弯中等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5723Sequencing Jobs Through Two MachinesThree jobs must each be processed first on Machine 1 and then on Machine 2, in that order. Each machine handles one job at a time, jobs cannot be preempted, and all jobs are available at time 0. Processing times (Machine 1, Machine 2) in minutes are: Job X = (3, 2), Job Y = (2, 4), Job Z = (4, 3). You may choose the order in which jobs enter the system (the same order is used on both machines). What is the minimum possible time at which all three jobs are completely finished?脑筋急转弯中等brainteaser未尝试面试订阅