Brainstorming Problems

Brainstorm on what windows (real windows—those brittle, transparent things in walls) will be like 200 years from now.  Assume great technological progress.  Money is no object.

Design the ultimate shower.  Assume money (and fear of electrocution) are no object.

Quizzes

You're in a rowboat floating in a tank of water.  There's a big rock in the boat.  You drop the rock into the water, and it sinks to the bottom.  Does the level of the water in the tank go up, down, or stay the same?  (I got this problem personally while sitting in the hot seat, and blew it. It's a cool problem.)

Describe an algorithm to determine whether a singly-linked list is corrupt.   By corrupt, I mean one node is  back linked to a previous node, so that if you start at the beginning and go node by node, you'll never come to a terminating node.  Don't allocate memory doing it, e.g., space for each pointer.  (Software can be beautiful.)

Describe a simple algorithm for reversing the order of words in a string.  For example, "The quick brown fox jumped" becomes "jumped fox brown quick The."  Do it in place, that is, without using a temporary or output string.

A rectangular birthday cake has a single rectangular slice missing, and you want to divide what's left equally between you and a friend, with a single straight cut.   How?  (No, you don't cut the cake horizontally—one of you wouldn't get any frosting.  There's an elegant answer.)

Why are manhole covers round?

Estimate how many gas stations there are in the U.S.

Estimate how many tennis balls would fit in the Rose Bowl.

Why did evolution favor egg-shaped eggs?