My guess:

The problem is one of discrete values. You are asking about "a boy", but there are no "a boy"s. There are only fractions of boys. The total sum of "boy fractions" is the same, but the number of pairs of "boy fractions" that meet the distinction of "a boy" changes. "A boy" does not vanish because there were never "a boy"s in the first place.

One might have better luck with "boy heads", and you can see that at roughly 5 oclock there is a "boy head" that turns into a "boy arm". So part of the trick is that some of the "boy fractions" change in your interpretation. Without the trick, you would reasonably say, "Wait, there is still a boy head there! So there are still 13 boys!"