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836Minimum Room Count 1Meetings occupy half-open time intervals [(9, 12), (10, 13), (11, 15), (14, 16)]. What is the minimum number of rooms needed so that all meetings can be scheduled without overlap?脑筋急转弯简单brainteaser未尝试免费837Minimum Room Count 2Meetings occupy half-open time intervals [(8, 10), (9, 11), (10, 12), (10, 13), (13, 15)]. What is the minimum number of rooms needed so that all meetings can be scheduled without overlap?脑筋急转弯简单brainteaser未尝试免费841Batch Shuttle Time 1A shuttle holds 5 people and takes 7 minutes for a one-way crossing. It must return after every outbound trip except the last. How many minutes are needed to move 23 people across?脑筋急转弯简单数值题未尝试免费846Periodic Window Alignment 1One maintenance window opens every 18 minutes and another opens every 24 minutes, both starting now. After how many minutes will they next open simultaneously?脑筋急转弯简单数值题未尝试免费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5699Sorting Five With Fewest ComparisonsYou must sort 5 distinct numbers using only pairwise comparisons, each of which returns which of the two compared elements is larger. What is the information-theoretic lower bound on the worst-case number of comparisons any comparison-based sorting algorithm needs, AND is that bound actually achievable for 5 elements? Give the minimum worst-case number of comparisons that guarantees a full sort.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5701Guess the Number 1 to 1000An adversary picks a secret integer between 1 and 1000 inclusive. You may ask yes/no questions, each answered truthfully, and you may choose each question adaptively based on previous answers. What is the minimum number of questions that guarantees you can determine the secret number in the worst case?脑筋急转弯简单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5703Eight Coins, One Known LighterYou have 8 visually identical coins; exactly one is counterfeit and is known to be LIGHTER than the rest. Using a two-pan balance scale (left-heavy / right-heavy / balanced per weighing), what is the minimum number of weighings that guarantees identifying the light coin in the worst case? Weighings may be adaptive.脑筋急转弯简单brainteaser未尝试免费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