Hint - 'Resign' is not the solution.
I can't see a way that out for white there tbh
@TheCalculatorKid - You are not thinking out of the box enough. Its a very left field solution.
@JimSheridan - Somewhere in what you wrote, you touched on what is the base for the solution to both the problems. You use something in connection to one of the things you touched upon in your post and use it as the base to the solution.
@JimSheridan - Every word you wrote is absolutely correct (except the no solution part)... and YET ... within the parameters outlined in the original problem, white has a very clever way out. 
Keep thinking 
What side of the board is what? With such a ridiculous position the first thing I need to know is which way the pawns are moving. I noticed that the only possible way to avoid checkmate is if the king is on h8...
Only possible solution; Kb2 and draw with 3rd repetition of position rule (but why black is not make check mate earlier..)
Pawn g6 to g7
If the king is on a1 in the second problem I’m done with this thread.... talk about an impossible position Jim
Let it time out and chess.com will give you a draw by insufficient material.
The board is from black's point of view. So White king is a1 in problem one and h1 in problem 2.
The critcism regarding board configuration is justified. I do apologise. Leaving co-ordinates on the board would have helped.
The boards in the OP have been fixed to be from White's point of view now.
To explain my answer. It is clearly stated that we are playing a game on chess.com and that we should think outside the box. On chess.com if you opponent has only a knight or a bishop then you can simply time out and it will be called a draw by insufficient material.
I agree with James. Letting the game time out is whites best “option”. Notice how he never asks for white’s best move. Good stuff James
