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Math Horizons - September 2003

Content Teasers for September 2003

Chance and Thunderstorms

Predicting the weather with math.

How to Ace Literature

A streetwise guide for the math student.

Fibonacci's Triangle and Other Abominations

Pascal no longer has the corner on triangles.

A Dozen Questions About: Sums of Powers

A powerful way of adding things up.

A Switch in Time Pays Fine

A quick way to double your money.

A Constant Regularity Observ'd

The origin of statistics.

Mother Knows Best

The power of exponential growth.

Slugbate Speaks

Colin Adams reveals his plaid side.

Finding Your Misteaks

A student reads "Misteaks...and how to find them before the teacher does."

Problem Section

S-78.

Proposed by Karl Havlak, Angelo State University. A bank offers two investment offers: m% compounded monthly for n months or n% compounded monthly for m months, where m and n are positive integers with m>n. Which offer generates more money?

S-79.

Proposed by Bob Harris, Boalsburg, Pennsylvania. A fellow graduate student at the University of Chicago of Raymond Smullyan, LLD (the Lion of Logical Deduction), had two brothers, aged six and eight. They found in Raymond's attic three abandoned logic machines, and converted them into Transmogrifiers. The Dogmatizer would change one dog into one cat and one rat. The Categorizer would change one cat into two dogs and one rat. The Rationalizer would change one rat into three dogs and one cat. Each machine would also work in reverse. Starting with Raymond's cat, the boys tried to obtain: a) some rats, but without any dogs or cats; b) some dogs, but without any cats or rats; c) more cats, but without any dogs or rats. For each task, either prove that it is impossible or find a sequence of transmogrifications which will result in the minimum number of animals of the specified type.

The Final Exam: The Inquisitive Problem Solver