It seemed like a coincidence, but just as Mr. Hilbert finished the checkout procedures at the front desk of the Grand Hotel, the lights went out.
"What happened, Mr. Cantor?" Mr. Hilbert asked the concierge.
"It's probably the fuse boxes," said Mr. Cantor rather disgruntledly. "I heard our manager fell for a late-night TV ad and bought these cheap fuses for the lights." Mr. Hilbert followed Mr. Cantor to the electrical room. Right at the front of the endless array of metal cabinets was one labelled "LOBBY AND FIRST $N$ ROOMS". On the ground were boxes upon boxes of "KIRK'S ZWEET DEEL FUZEZ $(1 \space \Omega)$".
"It's weird why we didn't switch to circuit breakers yet," said Mr. Cantor as he picked up a multimeter lying on the side. He made a grumbly noise. "Hmpf, seems like the multimeter is almost out of battery. We might not able to measure that many fuses before it dies". He opened the cabinet and grumbled some more. "And what kind of idiot doesn't label the fuses in a fuse box!" Peering at the fuses, his annoyance exploded into incredulity. "AND you can't even see the fuse wire in these fuses!!"
"It's ok," said Mr. Hilbert while mustering with his most soothing voice possible. "If we take out all the fuses and measure them together, we can minimize the number of measurements needed. Here's what we can do..."
Can you figure out the minimum number of multimeter measurements needed to find a single blown fuse $(R = \infty \space \Omega)$ from $N+1$ fuses before Mr. Cantor goes crazy? Can you also prove that your solution is optimal and works for all $N > 2$ ?