These problems use Knuth's up-arrow notation (http://en.wikipedia....-arrow_notation), with ^ being the up-arrow.
1. Find the smallest value for n, such that 1000^^n > 12^^(n+1).
2. We define the sequence g, by assigning g(1) = 3^^^^3, and g(n+1) = 3^^^...^3, where the number of up-arrows is g(n). A famously large number is Graham's number = g(64). Which is larger, Graham's number or 2^^^...^2, where the number of up-arrows is Graham's number?