logical math
Suppose a number of math contests is given each day over a $2$ week period. The winner of each math contest receives $17$ cents. Each non-winner is fined $1$ cent. The sponsor of the contests makes up the difference between the sum of the fines and the sum of the prize money presented for all contests. This difference is $3.60$ dollars. Cassidy lost $30$ cents. If they had $12$ contests a day for $2$ weeks as was originally planned, Cassidy would have lost even more. Each participant won at least $1$ contest but no $2$ participants won the same number of contests. The number of contests could not exceed $12$ for any given day. How many contests did Cassidy win?