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