None of those things are necessary to solve the problem. There's no need to search for information...all the information you need is contained in the problem. It's an exceedingly simple algorithm, and if you can't take the verbal explanation and translate it into code, you are simply not a programmer.

What would you search for, how to make a for-loop? If you don't know such basics as flow control and basic logic, you probably need to go back to school. If you can't remember the usage of printf then you either picked the wrong language, or ask for help, or simple explain you'll fudge it a little and a good interviewer wouldn't penalize you. I'd note if you are interviewing for a language-specific position and said you are fluent in it, not knowing such a basic API might count against you though...

I think the important thing you are missing is that generally in "whiteboard" type situations, you are not expected to produce a completely correct/compilable program. Generally pseudo-code or whatever language you please is accepted and if you make some small syntax or logic error it's not a big deal. In light of that, a compiler/IDE/computer is not necessary unless you have some other reason to require them...such as a disability.

The important part is to see how one reasons through the process of taking a described algorithm and translating it into code...that is the essence of programming. If you can't do it, you are ipso facto not a programmer.

Your analogy is false...in your example the person is not being tested on the actual job they are expected to perform. Obviously that's not a good test.

In this case the programmer is being tested on precisely what their day to day job is: taking a verbal description of a process and translating it into code....so an accurate analogy would be to ask an architect to sketch a simple truss structure and discuss it, which is not unreasonable.

The entire point here is to give a drop dead simple problem to weed out the people who are fundamentally unfit for the position.

Any programmer I want to work with will be able to walk up to a whiteboard and write a program to print a row of Pascal's triangle or a function that determines whether one string contains another. Simple programming problems like this are the tiny problems we solve on a daily basis; if you can't implement such trivial functions without bugs, how can you expect to design or implement multi-kloc systems without bugs?

Tom Marra's don't get hired at these big web co's kind of places.

This is probably the reason why there aren't many Tom Marra's at these big web firms and why don't seem to make any thing awesome anymore, than their first initial offering.

The job these algorithm kids in these big companies seems to do is to some ensure the wheels are rolling and they don't punctured. If they do, fix them by some fancy hackery!