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Here is a GIF image illustrating a supposedly "infinite" supply of white chocolate.

enter image description here

After watching this repeatedly, I can't definitively say why it doesn't add up. It clearly can't be infinite and the sizes of the pieces don't seem to be changed/edited. My guess is that the volume of the spaces between pieces somehow adds up to the final piece's volume.

However, the real question I have is: how have the dimensions of the array of chocolate changed? That is, if you start with a $6\times 4$ grid of chocolate pips, what are the final dimensions of the almost complete grid? I figure that height need not be considered because the cuts are made normal to the table surface.

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    $\begingroup$ generally, if you carefully draw (including finding the slopes of all relevant line segments) you find that the after picture has a slim empty part, probably triangular here $\endgroup$ – Will Jagy Jan 9 '15 at 2:23
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    $\begingroup$ en.wikipedia.org/wiki/Missing_square_puzzle $\endgroup$ – Deepak Jan 9 '15 at 2:23
  • $\begingroup$ What makes it an infinite bar of chocolate? $\endgroup$ – Ross Millikan Jan 9 '15 at 3:15
  • $\begingroup$ @RossMillikan Presumably, the OP meant inexhaustible (in supply) and not infinite (in span). $\endgroup$ – Deepak Jan 9 '15 at 3:54
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Well here's a picture:

enter image description here

Basically, the pieces that were moved end up being 1/4 shorter than they should be.

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  • $\begingroup$ This would be better if you highlighted the "grid" formed by the chocolate pieces. $\endgroup$ – Akiva Weinberger Jan 9 '15 at 4:03
  • $\begingroup$ @columbus8myhw Alright. $\endgroup$ – user1537366 Jan 9 '15 at 4:12
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enter image description here

The ending result is actually 1/5 of a piece shorter than the original bar. That amount(1/5) times 5 pieces across is equal to the extra piece

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  • $\begingroup$ This is not the same one as the OP's $\endgroup$ – user1537366 Jan 9 '15 at 2:38
  • $\begingroup$ This variation is very interesting. It is nice to see that the extra piece's area is easily verified. But what about the $6\times4$ case above? That one interests me more because the "perforated" lines seem to match up better all around. $\endgroup$ – Xoque55 Jan 9 '15 at 2:42

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