> Can I just admit I have no idea and just write down random numbers that aren't obviously wrong?

Seems fair enough to me, probably because thats what I do. At the end of the day nobody knows how long it will take unless they can tell the future.

I think scope is something my estimates are missing, for example if some one says their roof is leaking they may just need a broken tile fixed or they might need a new roof, without a proper scope of what I'm estimating the estimate is too open ended.