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I'm surprised nobody's given the obvious algorithm yet: while(i < BigInt(2).pow(10000)) ++i;

Before anyone complains, this algorithm is correct and does not break any of the rules as far as I can tell. :)

I think the timing attack is probably what he's really looking for.

Edit: as mattvanhorn pointed out, answer() is void, but that's ok... changed to a "constant time" algorithm. :)

The BigInteger is really big.

An i7 does about 109 gigaFLOPS, or 109 operations per nanosecond. [1]

Suppose we can do 1 guess per operation. There are 2^10,000 possible roots. [2]

2^10,000 / 109 nanoseconds is 5.804×10^2991 years. [3]

The stars will burn out before you brute force it.

[2] http://bit.ly/ZIWkkt (parens in the original link)

I must dryly point out that this does not invalidate the correctness of the algorithm.

As an optimist, I must point out that if Moore's law holds for the next 10000 doublings we'll have the answer in 20000 years, plus 9 picoseconds.

answer() has a void return, although I suppose you might be able to watch System.out to see if it worked.

Nobody said you had to stop after reaching that line ;)

Yup, just set a new PrintStream(new ByteArrayOutputStream()) in System.setOut() and you're good.