Spoiling the fun. So SPOILER alert:
Take two baseline datapoints, exemplified by one measurement, without the cans: You'll get the distance between (top of) floor and top of desk. Let's call this B (for the big distance of floor (being 0) to top of desk (T) ).
Now define two lengths: C for the height of a standing can, and W for the height of a lying can (its width).
Integral to this is the derived measurement C-W. Let's call this D (for difference).
Now for the difference between the tops of the bottom can standing and the top can lying you'll get B + C - (C-D).
Vice versa for the difference between the tops of the bottom can lying and the top can standing you'll get B + (C-D) - C.
The intuitive approach deceives you to make you forget about them as offsets as you're only measuring with a focus on cans. You're not measuring the difference between the width and the height of a can solely (in which case they would be (abouts) equal). you're adding those different offsets to an existing baseline. In the case where you exchange the offsets, this is not the case.
So sideways (for demonstration purposes assuming width is two third of height of can), you're substracting more of the internal part of B when the bottom can is standing, while you're not adding as much with the top can lying. The difference should always be (around) two times D (taking into account the relatively minor manufacturing variances.
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