3

I’m just wondering what one quick way, not the fastest, is reach a position where both sides have worked together to create a mutual stalemate here neither side could move on their turn, and the position is symmetrical.

2

There was a previous stack exchange answer which has a very amusing position where neither side can make a legal move.

Take a look - very enjoyable !

Mutual Stalemate

1

To be straightforward, there is no such thing as a mutual stalemate. Saying

neither side could move on their turn

is a bit confusing. If it's white's turn, then they can be stalemated. Black cannot be stalemated as well, because his opponent has not moved to put him in stalemate.

1

Seeing as this question has no proper answer, I've decided to answer it myself.

I found this in Journal Entry #361 on Tim Krabbe's website.

[Title "Gik, mutual stalemate in 37 ply, Shakhmatyi i Matematika, 1983"]
[FEN ""]

1.e4 d5 2.e5 d4 3.c3 f6 4.Qf3 Kf7 5.Qxb7 Qd5 6.Kd1 Qxg2 7.Kc2 Qxf1 8.Qxc8 Qxg1 9.Qxb8 Rxb8 10.Rxg1 Rb3 11.Rg6 Ra3 12.Rh6 gxh6 13.bxa3 Kg7 14.Kb2 d3 15.e6 a5 16.h4 a4 17.h5 c5 18.f4 c4 19.f5

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