It was a cold, silent night in the RED base. The mercs were all bundled up in bed, resting for the battle. Well, most of them. While his teammates were asleep, Engineer had been thinking. They were on a huge loosing streak, and he knew the Administrator was not happy with them. If they lost this next fight, something bad was almost sure to happen, and he didn't want to find out what exactly that was. So while everyone else had gone off to bed, he stayed down in his workshop.
Clearly, the sentries he had been building weren't enough to keep the BLU team away. No matter where he placed them and how hard he thought they were to kill, every sentry gun he built was easily destroyed by a well-timed Ubercharge or a Demoman's explosives. He needed bigger guns that did more damage and could take far more hits, and that's just what he was going to make.
Everything went pretty well until about 1:00 AM. He hit a snag when trying to work out some formulas concerning the sentry's design. Of course, Engineer was pretty good with math. He had to be in order to make effective structures. But this one little problem stumped him. The problem was a^n+b^n=c^n. He knew that this was true if n was equal to either 1 or 2, but he wasn't sure if it worked if n was any integer value greater than 2. He had a theory that it wouldn't, but proving or disproving it was a pain. Since there are a countably infinite number of positive integers greater than 2, he couldn't just test it out by plugging in every number for n. But if that wasn't an option, how else could he test his hypothesis?
After an hour or so of working on this problem, he decided to take a short break. He made his way over to the base's kitchen and grabbed a sandvich, noticing that Spy was up, too.
"Hello. What are you doing up?" asked Spy. "You should get some sleep. We've got a big fight tomorrow."
"Well, pardner, I've been tryn'a build a better sentry. But it ain't as easy 's I thought..." replied Engineer. "What're you doin' down here, anyways?"
"That's none of your concern."
"Oh... I see. Well... uh... You don't s'pose you could help me, could you?"
"'I don't suspect I could. You know much more about mathematics than I do. But I could try."
Just then, Sniper entered the room. "Oi, what're you lot on about? Some of us are tryin' ta sleep in here!"
"Howdy, Sniper! I've been tryn'a prove somethin'. See, I'm buildin' a better sentry gun, but unless I can prove that no three positive integers can satisfy the equation a^n+b^n=c^n for any integer value of n greater'n 2, I'm stuck. Spy and I were gonna see if we could solve it."
"Well, if the past foive minutes has been any indication of what the rest of your speculatin' will be like, I won't be sleepin' any more tonight. Maybe I can help."
After several minutes, the three mercenaries decided that they wouldn't be able to prove or disprove Engineer's theory on their own.
"Well, gentlemen, this clearly won't be an easy one to solve. Perhaps we should ask someone else for help?" Spy suggested.
"Couldn't hurt," responded Engineer. "But who?"
"Maybe Medic would know something about it."
"Oi, you can't be serious. That guy's bloody INSANE! He probably won't be any more helpful than anyone else!" Sniper exclaimed. "Besides, he'd have our 'eads for wakin' 'im up at 2:30 AM!"
"Well, it couldn't hurt to try!" replied Engineer. "Just as long as we get that bonesaw of his out of the room first..." he added.
The trio of REDs tiptoed through the hallway and into the Medic's room. Carefully, Engineer grabbed the bonesaw, but he wasn't quiet enough and woke Medic in the process.
"VHAT IS GOING ON HERE?!" he yelled, glancing around the room. "AND VHAT HAVE YOU DONE VITH MY BONESAW?!'
"Whoa, calm down, pardner. It's just us. We came to ask ya if you could help us with this math problem."
"AT 2:30 IN THE MORNING?"
"It's important, mate. The three of us couldn't solve it, so we reckoned you might be able to."
"Vell, you didn't have to sneak into my room and steal my bonesaw, dummkopfs! So, vhat's zis problem you need to solve?"
"Apologies. Anyway, we need to prove that no three positive integers can satisfy the equation a^n+b^n=c^n for any integer value of n 2."
"Do I have to?"
"Yes."
"WHAT ARE YOU NUMBNUTS DOING OVER HERE?" Soldier burst through the door, glaring at all of them.
"Well, you see-"
Engineer was cut off by a very angry-looking Scout. "Yo, some of us are tryin' ta sleep here! If ya gotta do your nerdy math crap, don't wake ALL of us up!"
"We can explain! I was tryn'a build a better sentry, but y'see, I ran into this one formula. We need to prove that no three positive integers can satisfy the equation a^n+b^n=c^n for any integer value of n 2, but none of us can solve this darn thing."
"Well, I'm goin' back ta bed. G'night, everyone," Scout called, strolling back across the hall.
"Ah well, we didn't need him anyway. Soldier, I'm sure you'll be much more helpful." Spy smirked, making sure he said it just loud enough for Scout to hear.
"Whoa dere. Slow down. Soldier ain't smarter than me!"
"Prove it!"
"Oh, it's on now. I'm gonna solve dis problem, just you watch!"
And so the six mercenaries began working on the problem, discussing mathematical concepts and using their prior knowledge to try to find a way to prove the devilishly difficult conjecture.
Meanwhile, Demoman had gotten up to go to the bathroom when he noticed most of his teammates sitting there with pens and paper in deep discussion about complicated-sounding concepts. "Aye lads, what're ye up to?" he asked, walking into the room.
"Oh, hello, Herr Demo! Ve're solving zis problem for Engineer! If ve do, ve might just have found ze key to victory!" Medic explained.
"That sounds complicated..."
"Oh, it is! But don't vorry, ve don't understand it either. You should join us!"
"What's the worst that could 'app'n? I'm in!" Demo announced excitedly.
"Heavy can stand no more of this. First, leetle Engie, Spy, and Sniper woke up doktor, who woke up Soldier and Scout. Then, leetle Scout and Soldier yell at all of you. Then, you continue making noise. What is wrong with you?"
"Mmmph mmmph!" agreed Pyro, who was close behind him. The two had been attempting to get some sleep ever since Spy, Engineer, and Sniper had woken up Medic, but every time they were about to doze off, a new loud noise came along.
"So, what is going on?"
The mercenaries explained the situation to Pyro and Heavy. They didn't seem impressed.
"You kept us up for MATH PROBLEM?"
"WATCH YOUR ATTITUDE, PRIVATE! THIS MATH PROBLEM COULD BE THE DIFFERENCE BETWEEN WINNING OR LOSING THE MATCH!"
"Calm down there, you two. Heavy and Pyro, y'all don't have to help, but we'd appreciate it if you did," Engineer interrupted.
"What's in it for Heavy?"
"Well, we might be able to win this next round."
"Okay. We are in."
And so the RED team all gathered around, pens in hand, discussing how they would solve the problem. Although they hardly seemed any closer to the answer than when they begun, nobody wanted to give up. Their losing streak had gone on too long, and none of them were about to let it continue. Every new number that they wrote down, every confusing rule, every formula seemed like it was getting all of them just a little closer to victory, and that kept them going. But soon, minutes turned to hours and the sun was beginning to rise, but they still hadn't solved it. The battle was going to start soon, but they were all too busy to notice. And even when "Game begins in 3, 2, 1" was announced over the loudspeakers in the base, they were too caught up in their calculations to go fight.
"Hey guys, where'd ya think dose REDs are? We're already capping mid here and they ain't showin' up," the BLU Scout commented.
"I reckon they're plannin' somethin', mate," Sniper speculated.
"Aye, y' don't s'pose they're hidin' 'round here?" Demoman chipped in.
"Well, we could take a look around..." Engineer suggested.
"A'right, you guys do dat. I'ma keep cappin' dese points. Maybe if we do it fast enough, dey won't have time to do anythin'"
Little did they know, the RED team had just made an incredible mathematical breakthrough.
"Hey guys! I think we solved it!" exclaimed Scout excitedly.
"Well, don't that beat all?" Engineer grinned. "I ain't gonna lie to y'all, that was a toughie."
"Ve did it! Good vork, everyone!"
"Mmmph mmph mmph!"
The mercenaries were ecstatic. They had finally solved the near-impossible question. They had solved Fermat's Last Theorem. But their victory was short-lived.
"You failed!"
Horrified, the mercs slowly began to realize that they had been working the entire match and given the BLU team an easy victory.
"Well, at least we still have our proof!" Engineer reminded.
Just then, the BLU Soldier walked in.
"HAH! MAGGOTS! YOUR PLAN SUCKED!"
One crit rocket and many wails of despair later, the mercenaries and their mathematics were blown to smithereens. All that was left of their precious proof was a couple torn, blackened shreds of paper which fluttered to the ground and became lost in the rubble. Engineer let out a pitiful little sob and the rest of the mercenaries glared at him.
"Congrats, hardhat! You cost us our victory!" Scout yelled.
"Well, THAT was a disappointment." Spy said flatly.
"Mmmph!" huffed Pyro.
"Fools! This isn't math class," hissed the Administrator. "We hired you to fight. Next time, try killing ONE of them. I'm firing you all."
All the Engineer could do was weep as the rest of the REDs yelled at him and beat him up.
And that is why they hire mercenaries who can't read, write, or prove complex mathematical theorems.