This one isn't so much maths as it is logic. Hope that's alright.

Bellow is a picture of fifteen gnomes divided into parts:


Rearranging the top two parts gives the following picture of forteen gnomes:


The question is: 'Why are there more gnomes in the top picture then the bottom?'

In the lower picture every gnome has an upper part and a lower part. While in the upper picture one has no lower part and one has no upper part, and these can be used to constiture an extra gnome.

CB

Thank you for your interest.
How do those two gnomes constitute a single gnome of regular proportion (relative to the rest of the gnomes)?

I studied the figures (that is I know by inspection).

CB

(look at the third and tenth gnomes from the right in the upper figure)