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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