In Jenga, when you are moving your block out and another block next to it moves, are you allowed to push the other block(s) back?
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According to the official 2000 version of the rules:
Since this rule includes the proviso before touching another block I take this to mean that you can't touch blocks after you have started to remove your block.
I believe it would be within the spirit of the rules that you could try and replace the block you started to remove, then try and remove the block you disturbed.
The key is that you can only touch one block at a time with only one hand.
You can only use one hand. you can touch multiple blocks at a time to support the tower to get a block out as long as it's only one hand as well. If you disturb a block while trying to get your block out, you may leave it there but it is recommended to fix it so the tower doesn't fall or leave the next player with a move.
In the situation where a block touching the block you are removing is so loose that it gets significantly moved while you remove your piece there isn't much point in caring about the second piece. All that really happens is you give the next player a very easy turn because they know a piece that will come out easily.
From a game play point of view there really isn't any difference in all the possible rules:
While it might be important to pick a rule, I can't see a huge strategic difference between them.