<p>It is a nice problem to have.</p>
<p>With this kind of difference, money should not be a factor in consideration. $80K for four years, you can cover partly by working on campus and your parents can absorb the rest.</p>
<p>What you really need to focus on, is that what you want to with your life. </p>
<ol>
<li>Are you interested in top level science research? This would be my only reason to go to Princeton, if I were in your shoes;</li>
<li>How competitive are you? You may end up in the middle of the pack in Princeton, but top notch in the other two schools, and the latter would be a more desirable position career-wise 4 years from now;</li>
<li>If I want to a safe career and comfortable life, Purdue’s deal sounds sweet to me;</li>
<li>As far as the academics goes, in any schools, one can make it as rigorous as it can be. That’s not the issue. The issue is that who are around you, and who you can discuss your ideas with. </li>
</ol>
<p>In 1962, a first year graduate student in Cambridge University, Brian Josephson made some calculation, and his supervisor, Sir A.B. Pippard guided him through the physics research. This became known as Josephson junction, and won him the Nobel prize in 1973. In the same year, a 4th year undergraduate student of the University of Science and Technology of China, Wu Hangsheng did a similar calculation, and nobody knew what to do with it. Many years later, the best use that Prof Wu found, was to make it an exam problem.</p>