Chapter 80: The Five-by-Five Magic Square

Countless possible questions flashed through Kent’s mind.

But after thinking it over, he felt that some of them would simply be unfair to the First Elder.

Although this world possessed a civilization stretching back more than ten thousand years, its development had followed a path almost completely opposite to that of Earth.

Here, what mattered most was faith, inheritance, and personal strength.

For thousands upon thousands of years, the foundations of society had barely changed.

Earth, by contrast, had entered its true age of explosive technological advancement only within the last few centuries.

Strictly speaking, it was only after the Industrial Revolution that human civilization on Earth truly began accelerating at an astonishing pace.

China, for example, had experienced thousands of years under feudal dynasties. There had certainly been periods of extraordinary prosperity and strength, but those glorious ages had long since passed, and the weaknesses of the old system had eventually become impossible to ignore.

Power and wealth had remained concentrated in the hands of a relatively small number of people.

Yet the progress of society depended, at least in part, on preventing the gap between the privileged and the common people from widening without limit.

Once that divide crossed a certain threshold, the entire social order could eventually be overturned and rebuilt.

It did not necessarily matter how powerful the army was.

After all, even the strongest army was ultimately made up of ordinary people.

The Twin-Star Continent, however, was entirely different.

Here, the people who controlled the lifeblood of kingdoms were precisely those powerful nobles.

And a great many of those nobles were themselves formidable warriors.

In other words, the ruling class possessed not only wealth and political authority, but also overwhelming personal strength.

Under such circumstances, changing the social order was extraordinarily difficult.

That was one of the reasons why ten thousand years of history had produced relatively little fundamental progress.

Scientific ideas, in particular, could easily be suppressed.

Of course, if one placed the title of “magical research” over the same work, the situation became completely different.

Then very few people would dare interfere.

Kent quickly made his decision.

“Since the First Elder has lived for such a very long time,” he said with a faint smile, “this junior will give you an extremely simple problem involving numbers.”

As he spoke, Kent crouched down and drew a square grid on the floor.

Five rows.

Five columns.

Twenty-five empty spaces in total.

“My requirements are very simple.”

“You must place the numbers one through twenty-five into these twenty-five spaces, using each number exactly once.”

He pointed at the grid.

“When you are finished, the sum of the numbers in every row must be identical.”

“The sum of every column must also be identical.”

“And the two main diagonals must have exactly the same total as well.”

Kent stood up and dusted off his hands.

“First Elder, you have two hours.”

“Please begin.”

The problem Kent had just presented was known on Earth as a magic square.

The simplest commonly encountered version was the three-by-three magic square.

The numbers one through nine were placed into a three-row, three-column grid so that every row, every column, and both diagonals added up to fifteen.

For example:

9　2

5　7

1　6

That was one of the most basic three-by-three magic squares.

Even such a simple puzzle had once troubled Kent for quite a long time when he was still a student.

He had spent ages working through it before finally understanding the method behind it.

But the problem he had just given the First Elder was not three-by-three.

It was a five-by-five magic square.

After explaining the rules, Kent calmly strode to one side, found himself a seat, and sat down.

This was not a problem that could be solved casually.

At first, the surrounding spectators had looked at Kent with obvious pity.

Almost everyone had assumed that the boy was doomed the moment he agreed to compete in knowledge with the First Elder.

But once Kent finished presenting his question, the atmosphere changed.

The crowd stared at the twenty-five empty spaces he had drawn on the ground.

One after another, they began silently calculating.

Trying possibilities.

Rearranging numbers in their minds.

Before even two minutes had passed, the way they looked at Kent had completely changed.

People often said that mages possessed the broadest and deepest knowledge of all professions.

Many had always been somewhat skeptical of that claim.

But now, after only a brief attempt at solving Kent’s problem, they suddenly felt that the question he had produced was so absurdly difficult that perhaps even the gods themselves would struggle with it.

The difficulty lay in one simple fact.

If even a single number was placed incorrectly, everything that followed could be wrong as well.

Without knowing the proper method, one could only continue testing combinations over and over again.

And there were twenty-five numbers.

Twenty-five positions.

Countless possible arrangements.

Forget two hours.

Without a known solution or a systematic method, they felt that even an entire year might not be enough.

On Earth, a magic square was little more than an entertaining mathematical puzzle.

In this world, however...

Heh.

It was no longer merely entertainment.

And Kent had been merciful.

He knew not only how to deal with a five-by-five magic square, but even much larger ones.

A twelve-by-twelve magic square, for example.

Kent had briefly considered using one of those instead.

But after thinking about it, he decided against it.

If he really gave the First Elder a twelve-by-twelve magic square to solve from scratch...

the old dark elf might still be calculating on the day he died.

The First Elder was completely dumbfounded.

At first, he had assumed that Kent would ask some question related to magic.

But when Kent announced that it was a mathematical problem, the First Elder had nearly laughed to himself.

Mathematics?

Was that not simply a matter of calculating numbers?

And when it came to calculations, there were few among the dark elves who could rival him.

So when Kent first finished explaining the problem, the First Elder had thought it sounded ridiculously simple.

Then he tried solving it.

Once.

Twice.

A few more times.

Before long, cold sweat began to bead across his forehead.

The more he stared at the empty grid on the floor, the more it seemed like a bottomless pit.

Every arrangement appeared promising at first.

Then one wrong number ruined a row.

Fixing that row destroyed a column.

Correcting the column threw one of the diagonals into chaos.

After several attempts, even the First Elder felt as though his mind were becoming tangled.

Still, he could not afford to give up.

Ignoring everything else around him, he grabbed a piece of magical glowstone and began scribbling calculations furiously.

Kent nearly laughed when he saw the First Elder’s expression.

Two hours?

If the old man managed to solve the problem in just two hours, Kent would have been genuinely impressed.

Back on Earth, who knew how many people had studied such mathematical puzzles before their underlying patterns were gradually discovered?

Countless people had probably burned through countless brain cells in the process.

In truth, everything in existence followed some kind of pattern.

The only question was whether anyone had managed to discover it.

From the movement of celestial bodies across the heavens to a single drop of water falling upon the ground, there were rules hidden within everything.

Kent suddenly had another thought.

Perhaps, if the contest reached the third round, he should give the First Elder a twelve-by-twelve magic square.

But...

Would that be going a little too far?

Kent sat there with a pleasant smile on his face while an intense debate raged inside his head.

If the First Elder had known what Kent was considering at that moment, he might very well have died of rage on the spot.

Two hours was neither especially short nor especially long.

And the First Elder was far from the only one scratching away at calculations.

Quite a few of the others had also found themselves unable to resist attempting the puzzle.

Somewhere along the way, one of the guards apparently leaked the details of Kent’s question to the people outside.

Before long, even the crowds gathered beyond the City Lord’s residence were discussing it.

Everyone wanted to know who would ultimately win.

On one side stood the First Elder of the dark elves, a man who had lived for more than a thousand years.

On the other stood Kent, a boy barely in his teens.

The dark elves naturally cheered for the First Elder in secret.

The dwarves, gnomes, and humans who had come from other cities, however, were largely hoping Kent would teach the old dark elf a proper lesson.

As far as they were concerned, the First Elder needed to learn that this was no way to treat someone who had saved members of his own race.

In truth, almost everyone felt that the First Elder had handled the matter poorly.

Yes, his status was lofty.

Yes, he was accustomed to standing above others.

But Kent had saved a great many dark elves.

Would it really have been so difficult to speak to him with a little courtesy?

The races of the subterranean world were generally straightforward by nature.

Even the humans who had spent years living among dwarves, gnomes, and dark elves had gradually become much more direct in temperament.

That only made them dislike the First Elder’s behavior even more.

Kent glanced around the room and found the expressions on everyone’s faces rather fascinating.

The First Elder was drenched in sweat.

Darkya’s face had gone pale.

The other dark elf elders remained silent, their expressions carefully controlled.

Still, Kent noticed something.

A faint trace of excitement lingered in their eyes.

As for what they were excited about...

Kent could make a fairly good guess.

There was an old saying from Earth:

Wherever there were people, there would be struggles.

Dark elves were no exception.

The dwarves, gnome, and humans, meanwhile, were no longer even trying to hide their smiles.

As the minutes passed, those smiles became more and more obvious.

Several of the dwarves even pulled out bottles of liquor they carried with them and began drinking in great gulps.

They said nothing.

They did not need to.

Anyone who was not blind could see that there was clearly some old tension between the dwarves and the dark elves.

At last, the two hours came to an end.

“Time’s up.”

Kent rose from his seat.

“First Elder, have you solved it?”

As he walked toward the First Elder, Kent was already wondering what kind of question the old dark elf would ask in the next round.

Despite his relaxed appearance, Kent was not entirely at ease.

There were still two rounds remaining.

The First Elder would set the question for the second round.

If the contest reached a third round, the right to ask the final question would be decided by drawing lots.

So Kent was still somewhat nervous.

At last, he stopped beside the First Elder.

The First Elder heard the question and slowly lowered the magical glowstone in his hand.

For a long moment, he stared at the mess of calculations before him.

Then he let out a long sigh.

“No.”

He admitted it reluctantly.

“I couldn’t solve it.”

“This round is yours.”

Then he lifted his head and looked directly at Kent.

“But I still have one doubt.”

His eyes narrowed slightly.

“Can you actually solve this problem yourself?”