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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701Three-Set Region Recovery 1In a universe of 140 objects, sets A, B, C satisfy |A|=62, |B|=55, |C|=49, |A∩B|=22, |A∩C|=18, |B∩C|=17, and |A∩B∩C|=9. How many objects lie in exactly one of the three sets? How many lie in exactly two? How many lie in none?脑筋急转弯简单数值题未尝试免费706All-Letter String Count 1How many length-7 strings over an alphabet of size 3 use every letter at least once?脑筋急转弯简单数值题未尝试免费711All-Server Assignment Count 1How many assignments of 6 labeled jobs to 3 labeled servers use every server at least once?脑筋急转弯简单数值题未尝试免费716Filtered Divisibility Count 1Among the integers from 1 to 180, how many are divisible by none of 2, 3, or 5?脑筋急转弯简单数值题未尝试免费721All-Category Coverage Probability 16 independent tickets are each assigned uniformly to one of 3 categories. What is the probability that every category appears at least once?脑筋急转弯简单数值题未尝试免费726No-Adjacent Ones Count 1How many binary strings of length 8 contain exactly 3 ones and no two ones are adjacent?脑筋急转弯简单brainteaser未尝试免费731Positive Composition Count 1How many ordered compositions of 10 into 4 positive parts are there?脑筋急转弯中等brainteaser未尝试免费736Lattice Paths with Fixed Turns 1How many lattice paths from (0,0) to (5,4) using right and up steps have exactly 3 turns?脑筋急转弯简单brainteaser未尝试免费741Committee-with-Chair Count 1From 8 labeled people, how many ordered pairs (committee, chair) are there where the committee has size 3 and the chair is a member of the committee?脑筋急转弯简单数值题未尝试免费746Multiset Word Count 1How many length-7 strings contain exactly 3 A's, 2 B's, and 2 C's?脑筋急转弯简单数值题未尝试免费747Route Through a Checkpoint 2How many lattice paths from (0,0) to (7,5) pass through (3,2)?脑筋急转弯简单brainteaser未尝试免费748Two-Stage Allocation Count 3How many ways can 9 identical tokens be split into 3 positive piles and then choose one token from the largest-index nonempty pile to mark?脑筋急转弯中等brainteaser未尝试免费