My Math Forum 2012 HMMT November - Guts Round

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 November 11th, 2012, 12:13 PM #1 Senior Member   Joined: Jun 2011 Posts: 164 Thanks: 0 2012 HMMT November - Guts Round I just participated in this tournament, note: the questions are fairly hard, do not feel bad if you could not solve some of them, and actually, if you could solve more than half of those, you are already amazing! The rules: work 3 at a time, after you hand in the 3 questions you were working on, you cannot get it back... ever. You start with questions 1-3, have 2.5 hours for the whole round, a total 36 questions, from easy to hard. the number in the bracket means the point value of the question (all or nothing except the last 3) Here are most of the questions (trying to find the rest of it): 1.[5] Find the number of prime numbers less than 30. 2.[5] Albert is very hungry, and goes to his favorite burger shop to buy a meal, which consists of a burger, a side, and a drink. Given that there are 5 different types of burgers offered, 3 different types of sides, and 12 different types of drink, find the number of meals Albert could get. 3.[5] Find the area of the region between two concentric circles that have radii 100 and 99. 4.[6] ABCD is a concave quadrilateral such that ?1(i). Write down a permutation of the integers from 1 through 7. Let N be the total number of answers submitted for this problem, and let n be the number of submitted answers your answer is superior to. You score will be ?20 n/N?. I will fill up the questions I left blank in near future since I could not find those problems for now. Note: some notations I used words instead of symbols, so they may look strange.

 Tags 2012, guts, hmmt, november, round

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