HMMT 2014 U35

How many times does the letter "e" occur in all problem statements in this year's HMMT February competition? If $C$ is the actual answer to this question and $A$ is your answer, then your score on this problem is $\left\lceil\max \left\{25\left(1-\left|\log _{2}(C / A)\right|\right), 0\right\}\right\rceil$.