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678Bitmask-and-Mode Repeat 3A trading engine state is described by a 4-bit flag pattern and one of 3 operating modes. What is the smallest number of snapshots that guarantees a repeated full state?脑筋急转弯中等数值题未尝试免费679Queue-Regime Repeat 4A simplified venue state is (bid queue mod 6, ask queue mod 6, regime among 4 labels). How many observations force a repeated full state?脑筋急转弯中等brainteaser未尝试免费680Automaton Visit Repeat 5A deterministic signal automaton has 81 possible internal states. Starting from any state, after how many visited states must some state have appeared at least twice?脑筋急转弯困难brainteaser未尝试免费681Length-and-Sum Congruence Window 1Given 13 integers a 1, ..., a 13, show that some nonempty consecutive block has length divisible by 3 and sum divisible by 4.脑筋急转弯简单derivation未尝试免费682Sector-Liquidity Tag Collision 2Each trade is tagged by one of 4 sectors and one of 4 liquidity buckets. Show that among 17 trades, two trades must share both tags.脑筋急转弯中等brainteaser未尝试免费683Venue-Session Tag Collision 3Each quote is classified by one of 3 venues and one of 6 session buckets. How many quotes guarantee that two quotes share the same ordered pair of tags?脑筋急转弯中等brainteaser未尝试免费684Parity-and-Desk Match 4On a floor with 5 desks, each ticket also has one of 2 parity labels. How many tickets guarantee that two tickets share both the same desk and the same parity label?脑筋急转弯中等brainteaser未尝试面试订阅685Calendar-Digit Collision 5A process tags each alert by one of 3 weekday classes and one of 5 last-digit classes. Show that among 16 alerts, two must share both tags.脑筋急转弯困难数值题未尝试免费686Twelve Updates in One Second 1Twelve quote updates occur in a 1-second interval. Prove that two updates are at most 1/11 second apart.脑筋急转弯简单数值题未尝试免费687Even-Length Inventory Window 2Given 10 integers x 1, ..., x 10, show that some nonempty consecutive block of even length has sum divisible by 5.脑筋急转弯简单derivation未尝试免费688Shifted-Congruence Block 3Given 15 integers y 1, ..., y 15, show that some nonempty consecutive block has sum congruent to twice its length modulo 13.脑筋急转弯困难derivation未尝试面试订阅690Repeated State in a 20-State Engine 5A deterministic trading engine is described by a state pair (inventory mod 4, cash-balance bucket mod 5). Starting from any state and recording one state per observation, how many observations are enough to guarantee that some state is seen at least twice?脑筋急转弯中等数值题未尝试面试订阅691Parity-Aligned Repeated 2-Block 6Show that every binary string of length 10 contains two identical consecutive 2-bit blocks whose starting positions have the same parity.脑筋急转弯简单derivation未尝试免费692Subset Size and Residue Collision 7Among any 36 distinct subsets of 1,2,3,4,5,6 , show that two subsets must have the same size and the same sum of elements modulo 5.脑筋急转弯中等derivation未尝试面试订阅693Smallest Sample for a Two-Label Integer Collision 8Each integer n is labeled by two features: its remainder modulo 5, and the parity of floor(n/5). What is the smallest N such that any choice of N integers must contain two with exactly the same pair of labels?脑筋急转弯中等数值题未尝试免费694Column Pattern Coincidence 4Nine binary columns each record a 3-day sign pattern. Show that two columns have exactly the same pattern.脑筋急转弯困难brainteaser未尝试面试订阅696Consecutive Block With Sum Minus Length Divisible by 9Given 9 integers a 1, ..., a 9, prove that some nonempty consecutive block has sum congruent to its length modulo 9.脑筋急转弯简单derivation未尝试免费697Consecutive Block With Sum Minus 3 Length Divisible by 11Given 11 integers b 1, ..., b 11, prove that some nonempty consecutive block has sum congruent to 3 times its length modulo 11.脑筋急转弯简单derivation未尝试免费698Subset Sum Divisible by 8 3Given 8 integers, prove that some nonempty subset has sum divisible by 8.脑筋急转弯中等brainteaser未尝试免费699Semicircle Load 4Twelve points lie on a circle. Show that some closed semicircle contains at least 6 of them.脑筋急转弯中等brainteaser未尝试面试订阅