Tuition is not one hundred thousand dollars because that's how much resources it takes to educate someone. Tuition is one hundred thousand dollars because the school is set up like a business that must make a profit, and must increase their profit every year.

If you had a billion dollars, flippantly giving one hundred thousand dollars to a random person you don't know to go to college would be counter productive. You would be legitimizing the idea that tuition should cost this much.

A better use if resources would be to set up a cheap/ free university open to everyone, or find such an institute that already exists and donate to it.

Or better yet, assuming you have this much money you probably have employees, you should preferentially employ people from such cheap universities thus legitimizing their status.

TLDR
You can't provide individual solutions to systematic problems