### Jenga

Posted:

**Fri Jul 29, 2016 6:22 pm UTC**Played this game with my son the other day and it got me thinking about strategy...

Jenga consists of a tower of rectangular blocks. Each level of the tower has three blocks in it, forming a square. The blocks on the next level up are rotated by 90 degrees, and so on. Suppose that the tower is 12 levels high, with 36 bricks total.

Version 1:

Two players take turns removing blocks from the tower until it falls over. The tower will fall over if the middle block + either of the side blocks are removed. So valid positions for any given layer are |||, |X|, X||, ||X, X|X. This will hold even on the very top layer.

Assuming both players play perfectly, is it possible for either player to devise a strategy that will guarantee a win?

Version 2:

When a piece is removed, it added to the top of the tower to either fill in the layer or create a new one. In adding to a new layer, players must add bricks in valid positions (ie. you have to put the middle block in first, then you can add the sides or add a new layer).

Assuming both players play perfectly, is it possible for either player to devise a strategy that will guarantee a win?

My solution to version 1:

I think there ought to be a solution to version 2, but I haven't worked through the variations yet.

Jenga consists of a tower of rectangular blocks. Each level of the tower has three blocks in it, forming a square. The blocks on the next level up are rotated by 90 degrees, and so on. Suppose that the tower is 12 levels high, with 36 bricks total.

Version 1:

Two players take turns removing blocks from the tower until it falls over. The tower will fall over if the middle block + either of the side blocks are removed. So valid positions for any given layer are |||, |X|, X||, ||X, X|X. This will hold even on the very top layer.

Assuming both players play perfectly, is it possible for either player to devise a strategy that will guarantee a win?

Version 2:

When a piece is removed, it added to the top of the tower to either fill in the layer or create a new one. In adding to a new layer, players must add bricks in valid positions (ie. you have to put the middle block in first, then you can add the sides or add a new layer).

Assuming both players play perfectly, is it possible for either player to devise a strategy that will guarantee a win?

My solution to version 1:

**Spoiler:**

I think there ought to be a solution to version 2, but I haven't worked through the variations yet.