You don't need to be able to generate the answer to your hard problem yourself, only to check that the superintelligence's offered answer is correct. These two abilities are equivalent if computing resources are unlimited, but you could run the superintelligence for a limited time... This line of thought seems to lead into the jungle of complexity theory and you should probably take my comments with a grain of salt :-)
The most simple, able to self-improve "seed" for a superintelligence must be how complex?
Give your (wild) estimation or a pure guess in the terms of bits.
Do you reckon it is 1000 bits enough? At least 1000000 is required? More than 10^20 bits?
I wonder what your approximate numbers are.
Thank you!