The coconuts problem in almost 80 chars:

perl -le'N:for(0..9999){$x=5*$_+1;for(1..5){$x=int($x*5/4+1);next N if$x%5!=1;}print$x;}'

I'm sure this can be improved, as I'm not much of a golfer (search Deja...), but it's still wonderfully evil. Note that the lower bound for where I have placed 9999 is good old familiar 1024... since bwtaylor has obviously taken a much more mathematical approach to the solution, perhaps he can enlighten us here. (And yes, I do have a non-obfuscated version of the above.)

Haven't gotten anywhere on the 12 coins problem. I once read a Piers Anthony book in which this puzzle played a semi-important part, so I'm sure the solution is rolling about in my subconscious somewhere.

If anyone wishes, I can type up the oracle problem...