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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5667Hat-Check Derangement CountSix guests check distinct hats. The attendant returns the hats in a random order. In how many of the possible return orderings does no guest receive their own hat?脑筋急转弯中等数值题未尝试免费5668Secret-Santa No Self-Draw ProbabilityFive people draw names uniformly at random from a hat containing all five of their own names, one draw each, forming a random permutation. What is the probability that nobody draws their own name?脑筋急转弯中等数值题未尝试免费5669Five Gifts Four Children SurjectionFive distinct gifts are distributed to 4 distinct children so that every child receives at least one gift. In how many ways can this be done?脑筋急转弯中等数值题未尝试免费5670Coprime-to-2357 Count up to 1000How many integers from 1 to 1000 are divisible by none of 2, 3, 5, or 7?脑筋急转弯中等数值题未尝试免费5671At-Least-One Fixed Point CountOf the 120 permutations of the labels 1,2,3,4,5 , how many fix at least one label in its original position?脑筋急转弯中等数值题未尝试免费5672Trilingual Survey None-CountIn a group of 100 people, 50 speak French, 40 speak German, 35 speak Spanish; 18 speak both French and German, 15 both French and Spanish, 12 both German and Spanish, and 6 speak all three. How many speak none of these three languages?脑筋急转弯简单数值题未尝试免费5673Totient of 60 by SieveHow many integers in the range 1 to 60 are relatively prime to 60 (share no common factor greater than 1 with 60)?脑筋急转弯中等数值题未尝试免费5674At-Least-One Couple ReunitedFour married women and their four husbands are randomly paired into 4 man-woman dance pairs (a uniform random perfect matching). What is the probability that at least one woman is paired with her own husband?脑筋急转弯中等数值题未尝试免费5675Seating with Forbidden Own-ChairFour people, each with an assigned chair, are reseated so that no person sits in their own assigned chair, and additionally person 1 must not sit in chair 2. How many seatings are valid?脑筋急转弯困难数值题未尝试免费5676Seven Tasks Four Machines All BusySeven distinct tasks are each assigned to one of 4 distinct machines. In how many assignments is every machine used at least once?脑筋急转弯中等数值题未尝试免费