# Problem 11

April 14, 2011

Two crouched behind Five and stared nervously out at the cliffs. The air was cold on his thin arms and legs. His snub nose felt like an icicle with cold and fear.

“Where are they?” The boy looked anxiously up at the old man beside him.

“They are here.” Five scanned the cliffs that surrounded them. “They cannot stay away, once I call them.” He raised his head and shouted, “Solution! Find the solution!”

For an instant, there was silence. Then, slowly, rocks began to roll down the hillside. Two squeaked with fright and ducked behind Five as their opponents climbed slowly down the opposite cliff.

A Nine came first, black wings flopping from its back. Its eyes burned with a cold light as it watched the two challengers. Behind it, a Four darted nimbly down the rocks. It was a savage beast, though too small to attack a master like Five. But a Nine—Two had never seen such a mighty being. Even Five was less powerful than that.

There were other, stronger things, Two knew from his studies with Five. Five had told Two of beings stretching up to the Greatest Possible, a master of such power that his name was unknown. But a Nine was still greater than humble little Two had ever imagined.

Five laid a hand on Two’s shoulder, speaking quickly. “Listen. If I fall in this fight—and I have never faced a Nine—you must carry on. Remember, you must find the solution.”

“Y-yes, sir.” Two stared at the Nine and Four, now standing at the cliff’s bottom. “They’re so big! Bigger than us.”

“No. We’re exactly equal, with the Unknown.” Five touched the small pouch at his side, the pouch without a lid that carried the Unknown. “And remember, you and I are both Primes. It’s how I have so much power, though that may not help me here.” He spoke even faster as their opponents began to advance. “Two, you must find the Unknown. Only then will our sides be equal.” Two nodded; he was too scared to speak.

The Nine reared up and roared, then exploded into a magnificent threat display. Two yelped and scrambled behind Five as the beast moved toward them, grown into a top-heavy improper fraction. Its black wings flared out; drool dripped off its long fangs. But Five stood firm and pointed at the Nine-Ones. “Simplify before solving!” he shouted. Even the Nine had to give way before that unbreakable rule. But as it shrank, Two caught a glimpse of a lidless pouch that hung at its side.

“Master, they have one too,” he whispered.

Five’s face went grim. “So I see.”

The Nine laughed. “So we meet, O noble Five. Who shall fight first? Your brat against my Four?” The Four snarled at Two, baring pointy teeth.

“No. We must fight first. It is the Order.”

“Fair enough.”

“Master, what are you doing?” Two whispered as Five stepped forward.

“Only what I have to.” Then Five threw back his head and called on the Power of Negative, that dangerous power which none may use without great risk. His shadow twitched, then moved swiftly. It separated from both the ground and Five and lunged straight at the Nine, eating into it. Black wings flailed. Then the shadow drew back and suddenly turned on Five. Two leaped forward, but before he could reach them both shadow and Five had vanished. He cried out in horror.

The Nine dragged itself off the ground. Although the Unknown still hung at its side, it had no more than a remnant of its former glory. When it scrambled to its feet, it stood no bigger than the Four crouching at its side. Two retreated until he felt the cliff at his back. How could he defeat the enemies that now watched him?

The Nine—Two still thought of it as a Nine, even though it was now no larger than a Four—pointed at him and shouted. The Four, which had hung back, snarling, throughout Five’s attack, leapt at Two’s throat. He fought desperately, trying to choke it. He felt its needle-like teeth in his skin.

The former Nine, now another Four, pointed at the two fighters. “Simplify!” it commanded in a voice that echoed down the valley. Two reeled back from the Four as a bolt of power struck him, knocking him to the ground. The Four stared for one instant at its master. Its face was contorted with the utter horror of being subtracted. Then it vanished.

Two stood up slowly. He was still Two; he could feel it. But he was empty now, hollow as a dry leaf. He was Negative.

He had scarcely realized this before the second Four flung itself at him. The pouch containing the Unknown swung wildly, hitting Two in the head as the Four reached him. They struggled. His new power was eating into the Four, making it, too, negative. Then he felt the sudden agony of division.

Two awoke slowly. A deep bass voice was proclaiming, “The Unknown is equal to Negative One-Half.” Slowly he pushed himself up. Once again he had changed. He was stronger than he had been as a Negative Two. He felt almost normal. Suddenly he heard a rustling on his shoulder. Turning, he saw a white owl. It cocked its head and stared at him with wise yellow eyes.

“Who are you?”

“I am One. You are Two. Together, we are the Unknown.”

Two raised his hand to his forehead and traced the mark x. He had found the solution. He was the solution. They had won.

Algebra, Lesson 43, Problem 11

5x + 2 = 9x + 4
5x + 2 = 9/1x + 4
5x + (-5x) + 2 = 9x + (-5x) + 4
2 = 4x + 4
2 - 4 = 4x + 4 - 4
-2 = 4x
-2/4 = 4x/4
-½ = x

Who knew algebra was so interesting?

Plotting this made algebra much more fun. . .