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Jenga is a game place with wooden blocks stacked on top of one another in an alternating pattern. Players take turns removing blocks from any layer and placing them on top.

As the game progresses the tower gets higher and higher until it collapses.

For a given configuration of blocks is there a way to calculate wither the tower is going to collapse?

I also want to know why some pieces are easier to remove than others...

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  • $\begingroup$ For each block, sum of forces equals zero and sum of moments equals zero. That's how you calculate the internal forces. $\endgroup$
    – John Alexiou
    Commented May 19, 2013 at 16:28
  • $\begingroup$ Note that small size changes affect the load distribution among neighboring blocks. $\endgroup$
    – John Alexiou
    Commented May 19, 2013 at 16:29

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The pieces that support the most weight have higher friction and are more difficult to remove. The easier it is to remove a piece the less important it is structurally. Each block needs to support the weight of all the blocks above it, and it has to have at least 3 contact points spread apart like a three legged chair. With two contacts points it will create a joint and the whole tower will collapse like in the neat GIF you posted.

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    $\begingroup$ Tiny manufacturing differences in size make up most of the difference between pieces. The bigger pieces tend to support more weight. $\endgroup$
    – Brandon Enright
    Commented May 19, 2013 at 16:39
  • $\begingroup$ My experience is that taking pieces from the bottom of the tower is usually much easier at the beginning of the game! $\endgroup$
    – Mark Mitchison
    Commented May 19, 2013 at 16:43
  • $\begingroup$ @MarkMitchison It's hard to see why, though. The weight of the tower above them remains essentially constant. If anything, it's the top blocks that should be easier at the start. $\endgroup$
    – Emilio Pisanty
    Commented May 19, 2013 at 18:37
  • $\begingroup$ @BrandonEnright, I agree as you can see from my comment on the OP. $\endgroup$
    – John Alexiou
    Commented May 19, 2013 at 20:04
  • $\begingroup$ @EmilioPisanty Quite, my point was that probably most blocks don't actually have to support all of the weight of the blocks above them. Perhaps Brandon Enright's suggestion about differences in size (and probably also shape: they are not all perfect cuboids) is the reason for this. $\endgroup$
    – Mark Mitchison
    Commented May 20, 2013 at 23:09
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For a given configuration of blocks, the COM of all the blocks over any block ( or pair of blocks )must not be outside the corner of the block beneath it.

For example here:

enter image description here

The blue dots are approx. COM of each block-pair Then the effective COM of the first 6 block-pairs must lie in the region above the 7th one (from top).

Whenever this condition is not valid the system only above it falls.

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