Matching question.

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I'm getting dizzy reading your post. Bottom line, rank your programs in order of preference. The rest is not under your control.
 
Assuming only one candidate can go to each program, everyone except candidate B gets their top choice since everyone was ranked by each program. Candidate B gets knocked down because Hopkins prefers candidate D, so they go to their next choice of Vanderbilt
Candidate A rank order list:
Harvard


Candidate B rank order list:
Hopkins
Vanderbilt


Candidate C rank order list:
UCLA


Candidate D rank order list:
Hopkins


Candidate E rank order list:
Upenn
 
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