Impossible chess challenge?

You are absoultely correct, there are many ways that this can be solved (zugzwang for example) , but to actually come up with a position is difficult.

Does it have to be chess or can it be chess960?
Also are there any rules like that the pawn formation has to be possible in a game, or things like a repeated bishop of the same, colour, I think the challengue its extremely difficult if not impossible, but Its extremely fun You can create all type of crazy positions, thanks for the idea!!

As a joke
lichess.org/editor/rbrb2k1/p1p1p1p1/PpPpPpQp/1PpPpPbP/1qPpPpPp/3PpBpP/4PpPp/1K6_w_-_-
Forget the challengue for a moment and pick up the board
and put random pieces, It is amazing how many things appear
that do not appear on a normal chess game.

It does not even apply to the challengue, there is no need to check but I am finding some crazy positions,
now I have a new hobby thank you man.

This position for example is incredible crazy but with the 1 8 change so that the pawn promotes
lichess.org/editor/1r4b1/8/8/nPP1P3/8/2kbP1N1/1PbP4/K1R4Q_w_-_-

Hahaha your welcome .

This is my best shot
lichess.org/editor/k7/p7/Np1N4/8/8/nP1n4/P7/K7_b_-_-

Both have perpetual check. Not giving check loses a pawn. But the endgame is probably still a draw

Wow optokopper! that really work! brilliant and great job!

lichess.org/editor/k7/p7/Np1N4/5p2/5P2/nP1n4/P7/K7_b_-_-
is probably even better. In my previous answer Ne1 for Black or Ne8 for White could be possible.

According to Shredder, the new position isn't draw by perpetual, but it is draw, the first position works though.