Geeks beware

[jon-nyc]

This is very unsatisfying.

[Doctor Phibes]

That's horrible. It can't be right.

My kids will be telling me their bedrooms are 'optimally tidy' next.

[Klaus]

I'm confused by the word "known".

This is just a lower bound, then? How pathetic.

A true computational geometrist would prove that this is the optimal solution.

[Horace]

The top right one has some room to wiggle, therefore there are an infinite number of such solutions.

[89th]

I tested, indeed the 16 blocks can fit, but not 17 if you line them up normally. The area of the square is 72.8-whatevers. Now if you actually reduce the area but make it a tad more rectangle (67.2-whatevers), you can fit 20 squares, as you'd expect.

[89th]

Much more efficient use of area, with no gaps that could cause movement damage during shipping.