As some of you know, I planned to grade your first homework on my business trip this past weekend. Following my stay in luxurious Newark, I boarded my flight home and relaxed into my seat. Shortly after take-off, I brought out the homeworks and commenced to grade.

The flight began simply enough, and our passage was peppered with occasional banter from the cockpit and flight crew. Early as it was, there was an expectant but pleasant attitude among the passengers. Some perused the informative, gerund-free flight magazine. Others listened to music, conversed, or snoozed. I sat confined by my tray-table in its lowered and unlocked position, sandwiched between two serendipitous travelling companions, whose identities were as yet unrevealed to me. I reverently removed my red grading pen from my briefcase.

At first, I graded like the gentle shepherd, guiding his flock toward their destination. I painstakingly inscribed corrective yet supportive comments onto your homework solutions.

Then, without warning, the captain interrupted our languor to inform us of the severe, imminent turbulence reported by planes advancing along our flight plan. Admittedly, I am not the most unflappable flyer. Although I enjoy roller coasters at amusement parks, I prefer such entertainment well below 20,000 feet. Glancing through the portal at the churning skies outside our cabin, I begain to share the captain's concern. I took a moment for spritual inventory, then returned to my grading with a new resolve. Minor infractions loomed large, as my red pen took on a life of its own.

"No induction hypothesis," I muttered aloud, stealing a nervous glance at the stormy skies. "Don't they know this could be the last proof I ever grade?" Suddenly, my neighbor on the aisle sprang to life. Irving, the travelling salesman---the very one for whom the combinatorial problem was named---began to pour out his heart. He related the story of the nephew of the great grandfather of his child's first cousin, twice removed. "He was like a brother to me," sobbed Irving. "It started small---some missing assumptions, a short-cut here and there, mostly in proofs by contradiction. Harmless, so he thought. If only it had stopped there. But he went on to the hard stuff: circular reasoning, backward induction---you can imagine how it goes." Comforting him, I asked where the poor boy was now. "He's doing 10 down in Ossining for practicing logic without a license. So sad, if only he had been set on the right path in college. If only his professors had cared." A fire begain to burn in my chest. Perhaps it was the Velveeta muffin served just after boarding. And yet, it seemed something more.

Irving was inconsolable. Overhearing all this, my neighbor at the window could no longer keep silent. "Oy," cried the revered rabbi from Hoboken. "Such a schande! My Moishe, such a good boy, a scholar, such promise. He could have been a computer scientist, a theortician maybe. But would he listen to his father?" He stroked his beard, deep in thought. Turning to me, eyes ablaze, he shouted "Justice, justice shall you pursue." And he tapped on the homework papers. The salesman drew himself out of his misery. "Faster, faster --- you must cover that territory at all costs!"

I knew then what I had to do. Sparks flew from my pen, as my comrades helped me find flaws in the proofs. "False implication, examples given instead of a proof" sighed the salesman. "Assuming the conslusion, three cases overlooked," clucked the cleric. Straightening himself in his seat, the salesman trumpeted "He who hesitates is lost!" and he picked up a red pen. "Out of sight, out of mind," granted the rabbi, joining the frenzy.

The flight attendant stumbled past, armed with fat-free pretzels, air sickness bags, and vintage magazines. Seasoned as he was, the drama unfolding in our row moved him to tears. "Such heroism," he wept, "and in the face of certain danger. Surely, one of you must be faculty at a great university." Braving the rolling cabin, he dashed away only to return shortly with ice for my aching arm, more red ink, and a bag of salted peanuts. Exchanging knowing nods, we attacked the homework papers with renewed zeal. Such was our concentration that the smooth descent and effortless landing went unnoticed in our row.

The window now offered a view of a typically beautiful St. Louis day. Composed once again, we lowered our gaze to the carnage of graded papers. My new colleagues shifted uncomfrotably away from me in their seats, avoiding my stare, as we taxied toward the gate. "Judge not, lest ye be judged," shrugged the rabbi. "Caveat emptor" sang the salesman, intently sizing up his latest commissions report.

What had I done? In my quest for justice, had I been too harsh? The flight attendant could not hide his disgust as I disembarked. "Have a nice day!" he taunted, as news of my misconduct spread throughout the terminal.

I exited the concourse and entered baggage claim, already awash in a sea of apparently similar suitcases. Desparate for inspiration, I startled when the loudspeaker intoned "R.M. Thrall, paging Professor R.M. Thrall, would you please answer the prayers offered in baggage claim?"

Of course, why hadn't I thought of this before? At Rice, when our proofs erred and our logic waned, Professor Thrall allowed us to recycle our homeworks. In fact, we measured homework-repetition tedium in units of Thralls.

So, I am offering you the same opportunity. You may recycle your homework and each cycle will give you up to 90% of the credit you could have received on the previous cycle. So, you can still make 90% on this assignment by perfecting it and turning it in again.