Patrick Reany
Disclaimer: Many of the following problems were taken from SATs or old
Olympiad tests. My alternative solutions may not follow Olympiad rules, however.
The techniques I use may not be fit for use in Olympiads or entrance exams or the like.
I believe that it's good to see alternative solutions to better fill out one's
mathematical abililties. Four decades ago, I quipped that one cannot truly
understand a theorem until one is able to prove it in essentially two different ways.
It's meant to be a thought-provoking claim, perhaps containing a morsel of truth.
Link to the first set of problems at First set of problems.
Link to the second set of problems at Second set of problems.
Link to the third set of problems at Third set of problems.
Link to the third set of problems at Fourth set of problems
Link to the third set of problems at Fifth set of problems
Link to the third set of problems at Sixth set of problems
As of set three, I have broadened the scope of what mathematics I treat for the reader.
Special Topics.
The Stoichiometry Problems are primarily on Problem Sets 4 and 5.
It now includes general topics which include abstract algebra, partial differentiation,
integration, thermodynamics, Babylonian algebra, and much more, in time. It also
continues to contain more traditional problems in competition mathematics
and complex numbers, mixed in.