Caturday Post: Tamerlane the World-Conquering Sword and the Fifty Thousand Puffballs of Persia*

In the ongoing (we desperately hope not dropped) anime series Arslan Senki, the main tank character, when told by the strategist that with the addition of two more allies they will only have to defeat 50,000 Lusitanians apiece, considers this and says completely seriously that he thinks he can take 50,000. (And we think so too. He's invincible as only a legendary hero can be.)

Obviously Elisheba's little orange cat Tamerlane, as the World-Conquering Sword of hopelessly spoiled and pampered indoor cats, can defeat 50,000 of his puffballs. 

some of Tamerlane's puffballs

But how much room in our house would these 50,000 puffballs take up?  We did the math:

Assume that a typical puffball is 3.5 cm in diameter. We'll assume the puffballs are un-squishable, and, further, we'll assume they are cubical with a side of 3.5cm rather than spherical in order to do a quick and dirty space estimate rather than getting sucked into a minimal packing arrangement problem. With all our simplifying assumptions this becomes an exercise in dimensional analysis:

volume of 1 puffball * convert to meters for easier visualization of space required * number of puffballs \[\frac{(3.5cm)^3}{1 puffball}\cdot \left(\frac{1 m}{100 cm}\right)^3 \cdot \frac{50,000 puffballs}{1} \]
\[=\frac{3.5^3\cancel{cm^3}}{1 \cancel{puffball}}\cdot \frac{1 m^3}{100^3 \cancel{cm^3}} \cdot \frac{50,000 \cancel{puffballs}}{1} \approx 2.1 m^3 \]
Thus we need 2.1 cubic meters of space for the 50,000 puffballs, or a box \(2.1^{1/3} \approx 1.3\) meters on a side.

Considering that the puffballs actually squish considerably, we can probably get away with one extra-large moving box from Home Depot and drop Tamerlane in on top to wreak havoc.

"Cry havoc, and let slip the kittens of war!" -William Shakescat


*like the bowmen of Persia, but puffier and significantly less likely to fight back in any way.