alt Hacker NewsHetzner rents you 42RU for €199 plus power and network. If we assume they can fill the entire rack, that's 4 9RU units for about €50 plus power and network.
If we assume an average power draw of 20W per laptop, that's 300W for each 15 laptop unit, or about €57/month in Hetzner's Finish DC (including aircon)
Not sure about network. A 1Gbit uplink with 10TB traffic (and €1/TB after that) is provided. Upgrading that to 10Gbit is probably similar to the €51/month cost for the same uplink for dedicated servers, so another €15 for each 15 laptop unit. Plus around €2/month/IP, but you can probably bring your own if you find a cheaper subnet to buy
So yeah, you are right that the math does not work out. But it is pretty close to break even. I think you can break even on this if you find a more space efficient way to cram them into the rack and don't pay yourself any salary