The Stack

Think you still got what it takes?
Caltech alumni who are currently professors on campus have shared some problems for you to solve.

Use the comment section for each problem set as a discussion board to collaborate with your fellow alumni.
When you're ready to check your answers, solutions can be found at the end of each problem.

Back to the Future

In December 2015, a new law titled “Low Volume Motor Vehicle Manufacturers Act” (H.R.2675) was introduced in the U.S., which creates a reasonable regulatory structure allowing small companies to produce a limited number of completed replica motor vehicles that resemble the appearance of cars produced 25 years ago or more. Suppose that upon finding this out,
you dish out all your savings (plus a loan from your parents) and buy a DeLorean.

Chances Are

The answer to the following question is more interesting than the question itself. Consider the experiment of tossing a
fair coin until you get two consecutive
heads. What is the probability distribution
of the number of tosses?

Up

Consider a He-filled balloon with a volume of 1 cubic meter. At 25°C and 1 atmosphere pressure, can you hold it without floating away?


Bonus Problem: Self-Heating Container

OnTech, a San Diego startup company, has developed self-heating containers for meals and beverages.
These containers will heat coffee to an optimal drinking temperature of 145 degrees F within minutes after pressing a button.