Fall Newsletter Is Up!

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Actually, it’s been up for almost a month, but I’m just now getting around to telling anyone.  See it here, and as usual, it’s probably more interesting for our current students and alumni than others.  But also as usual, we have a few fun problems to ponder:

Problem 5.1.1: (2000 AIME I) Let a, b be relatively prime positive integers and suppose that the coefficients of  x^2 and x^3 are equal in the expansion of (ax+b)^{2000}.  What is a+b?

Problem 5.1.2: An envelope contains 12 bills: 3 ones, 3 fives, 3 tens, and 3 twenties.  Two bills are drawn at random without replacement.  What is the probability that their sum is at least $20?

Problem 5.1.3: (From a Martin Gardner collection) An absentminded teller switched the dollars and cents when cashing a check for Mr. Brown. After buying a 5-cent newspaper [this is an old problem], Mr. Brown found that he had exactly twice as much as his original check. What was the amount of the check?

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