*Last time, on Patman: the inanimate series:*

Patman: You'll never get away with this, Puzzler...Puzzler: Hahaha, try this one! [writes something on the chalkboard]

Noggin: Holy Hadamard matrices Patman! It's a quadruple integral over a Klein bottle embedded in 4-dimensional hyperbolic space!

Patman: Ungh...if...I...could...only...reach...for...

*And now, the conclusion of "Double Induction":*

Patman: ...my...Pat Futility Belt (TM) (not available in stores! order now!) ...and...get...my...Table...of...Rainy-day...Integrals...

Noggin: Wait, Patman! It simplifies down to exp(-gamma) by symmetry! Intuitively obvious...You're no match for the Dynamical Systems Duo, Puzzl-- He's gone! What do we do now, Patman?

Patman: Quick, Noggin, to the PatMobile!

Noggin: But wait, neither of us can drive! And my learner's licence is only class Pi, no trucks, motorcycles, or ultra-high-tech-armor-plated-voice-controlled-fuzzy-dark-blue-cars-with-positive- Schnirelman-density.

Patman: Wait a minute, then how did we get here?

Noggin: Don't you remember, our grad student Derfla drove us here...But he's working on his PhD thesis right now...

[Meanwhile, at SFU, in the Pub]

Derfla: Argh, I lost again! Oh well, here goes another quarter...Hmmm, wasn't there something I was supposed to be doing? Nah...

[Back to our heroes]

Patman: Hey, I have an idea...I'll use my patented PatTopologyModifier and change the Euclidean metric to a discrete one! Then all distances will be the same, and we can walk there in one step.

Noggin: Leaping limits, Patman, that's brilliant!

[Moments later...]

Noggin: Wow, Patman, that was one non-differentiable ride!

Patman: Non-differentiable? Felt more like non-Lebesgue integrable!

Noggin: Definitely not Lebesgue, but maybe Generalized Riemann...Hmmm...

Patman: Now where's that dastardly villain Puzzler?

Voice of Puzzler: You solved my last problem, now try this one! Find a 2-regular subgraph with the same vertex set!

Patman: What? This graph has 1000 vertices, and finding Hamilton cycles is NP-complete!

Noggin: Then there's no hope...

Patman: But wait! He didn't say it had to be connected! That means we only need to find a 2-factor! Easy...

[The Puzzler suddenly leaps down from the ceiling and scratches his head]

Puzzler: What? That's impossible! Oh wait, I didn't say connected! No problem, I still have some tricks up--Hey, what?!?

Patman: We've got you now, Puzzler...Quick, Noggin, tie him up with a Conway knot.

Noggin: All done...Hey, who's that?

Patman: It's the Pencilguin!

Pencilguin: That's right, and I have some invalid proofs...Like this:

0*1 = 0*2, therefore 1 = 2.1 = sqrt(1) = sqrt((-1)^2) = (sqrt(-1))^2 = i^2 = -1.

[Noggin slumps to the floor, unable to withstand the horrible fallacies]

Patman: Hey, wait, you can't divide by 0! And square roots do not extend to the complex numbers while preserving multiplicativity!

[Noggin recovers, partially...]

Noggin: Let's see, where's the Patman Official Archenemy Handbook...A... G... Q...P...Pencilguin, here it is! It says that his weakness is number theory! Alright, Pencilguin, take this:

Prove Euler's theorem, Gauss' Law of Quadratic Reciprocity, Dirichlet's theorem, the Rosser-Schoenfeld inequalities, the Prime Number Theorem, Mordell's conjecture, the Extended Riemann hypothesis, Goldbach's conjecture, the ABC conjecture, the Prime k-tuple conjecture, and Fermat's Last Theorem!

Pencilguin: Arggggh! I can't!

Patman: Good work, Noggin! Let's go back to the PatCave. I'll get the PatTopo--

Noggin: On second thought, I think I'll take the bus...

*Next time, on Patman: the inanimate series: The Return of Jacobier*

*Burnaby, B. C., Canada*

*August and November 1993*

*(P.S. Can you spot the factual error in one of the episodes?)*