Registration is Open! Hello everyone, We are excited to let you know that registration for the 2022 Berkeley Math Tournament has now opened! You can register through our website, which is where you can also find further information on the contest itself. We will be holding an in-person tournament for BMT 2022 on Saturday, November 5, on UC Berkeley campus. This …

Instructions: This tiebreaker contains 5 short answer questions. All answers are positive integers. You will submit answers to the problem as you solve them, and may solve problems in any order. You will not be informed whether your answer is correct until the end of the tiebreaker. You may submit multiple times for any of the problems, but only the last submission for a given problem …

3. Let S be the set of all non-degenerate triangles with integer sidelengths, such that two of the sides are 20 and 16. Suppose we pick a triangle, at random, from this set. What is the probability that it is acute?

Instructions: This test contains 27 short answer questions, split into 9 sets of 3 questions. All answers are positive integers. Only submitted answers will be considered for grading. No calculators. 1. Julia and James pick a random integer between 1 and 10, inclusive. The probability they pick the same number can be written in the form m , where