*** SPOILER ***
Explained to me this way:
Think of them all in a line vs. interspersed like the graphic above.
You have 12 people. From person one you take a bit of scalp, from person 2, a bit more of the head....from person 12 all but the bottoms of their feet. You can simulate this by drawing 12* identical people in a row and drawing a diagonal line through all of the starting to the left of the left person's upper head and ending to the right of the right persons soles of feet.
Then move the upper chucks all one inter-person distance to the right. Sure, the guy on the left is missing a little hair, and the guy on the right is missing a bit of feet (and everyone in the middle is missing a bit of core), but now you have 13 people!
The graphic above leveled the diagonal line by putting the people in a diagonal instead, and then shuffled the people in a pattern that allows a swap vs. a shift, that also obscures the trick!
-brendan
* fixed a reference to 13 above to say 12.
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