Battle of Intellect

In order to demonstrate the fairness of the competition, Merlin and Arkhan each selected three challenges, totaling six in all. The side that won the most challenges would be declared the overall winner.

Merlin didn't hesitate and took the lead in proposing the first challenge, clearly intent on asserting his dominance over Arkhan.

He gently tapped his staff on the ground, creating ripples of light that spread outward and instantly enveloped the three of them. The surrounding scenery underwent a dramatic transformation, twisting and morphing in a peculiar way.

Arkhan gazed ahead on the vast, boundless plain, facing Merlin. In front of each of them stood an army of several hundred soldiers.

"For our first challenge, let's test our military strategy! Each side has five hundred soldiers, and the side that loses all of their soldiers first will be the loser." Merlin sported a sly smile on his face. "As a king, it's imperative that you can lead your troops to victory on the battlefield. Since you've questioned my teaching methods, let me see just how skilled you are."

"That's why I say you have no clue in this area. People trained through your methods can only be called generals, miles away from becoming a true king." Arkhan scoffed. "But since you want to play, I'll humor you."

Several hours later.

Merlin looked at the bodies strewn across the field, his eyes filled with disbelief.

"I... lost?"

He gazed across the battlefield and saw that Arkhan had only a few dozen soldiers remaining.

Although both sides had suffered heavy casualties, according to the rules, Arkhan had indeed won.

Reflecting on the battle, Merlin keenly realized the reason for his failure.

It was the formation!

Artoria stood beside Arkhan, her azure eyes filled with equal amazement. Merlin had personally taught her strategy, and in this illusionary realm, they had played countless games, with her mostly losing.

So she knew just how skilled Merlin was in this area.

But even so, Arkhan had defeated Merlin.

Just like Merlin, she had also discovered Arkhan's winning secret—formation!

It was a formation she had never seen before, but its effectiveness was unexpectedly remarkable.

Arkhan let out a sigh of relief.

In truth, he had no knowledge of military strategy and had never commanded a real war before. Fortunately, he possessed the wisdom accumulated from thousands of years of human civilization.

As Artoria and Merlin had suspected, his winning secret was indeed the formation.

He had chosen the Mandarin Duck Formation used by the Ming Dynasty. Ten soldiers formed a group, with two at the front, followed by the wolf brush soldier, two pikemen, and a trident soldier.

This formation not only maximized the strengths of long and short weapons but also provided great flexibility, making it the pinnacle of small-scale formations in the era of melee combat.

Arkhan's strategy was straightforward. Since he was not skilled in commanding a large number of soldiers, he decided to split them up and let them fight individually.

However, the idea was one thing, and reality was another. In practice, it didn't go as smoothly as he had imagined.

First, there was the issue of weapons. The wolf brush soldier used a three-meter-long sturdy bamboo pole, sharply tapered at one end and with hard branches left around the perimeter. It was a highly effective weapon.

Unfortunately, Arkhan couldn't find such weapons among his troops, not even suitable substitutes. So, he had to reluctantly abandon them.

Then came the issue of experience. It was his first time commanding troops on the battlefield, and while it didn't descend into chaos, he did fumble for quite a while. After one battle, he felt even more exhausted than he would have in a one-on-one duel against Scathach.

If Merlin had added more soldiers, he might have lost.

There were several factors that contributed to his narrow victory.

First, Arkhan employed a military tactical formation that Merlin had never seen before in an attempt to catch him off guard. Since he had anticipated that Merlin might be familiar with formations from the West, he decided to use one that originated from the East.

Second, this was an illusion created by Merlin, so Arkhan could easily command those soldiers with ease. But in reality, there wouldn't be so many obedient soldiers at his disposal. After all, this was an age where individual strength reigned supreme, and the idea of strict military discipline was a distant one.

But in any case, Arkhan was satisfied with his victory in this first round.

Now it was his turn to propose a challenge.

"Come on, tell me what you want to compare. It's okay, no matter what you want to compare, I'm fine with it~"

Merlin said those with eyes gleaming with excitement, not at all depressed by his loss in the first round. At this moment, he was filled with long-lost excitement, the last time he felt this way was when Artoria was born.

"Second round, we won't compare anything." Arkhan extended three fingers and grinned, "I'll ask you three questions, and if you answer two of them correctly, you win the second round."

Artoria couldn't help but glance at Arkhan. Whenever her teacher tricked Kay like this, he would wear the same mischievous smile.

"Oho? So you have some questions you'd like to ask this most famous and greatest mage? No problem, I will open my warm heart and help you without reservation~" Merlin confidently replied. He was, after all, Britain's most renowned mage and sage, hardly anything happening in this land could escape his eyes.

"First question—Three people went to stay overnight. The innkeeper said it would cost 30 coins for one night. The three of them discussed and decided that each one of them would contribute 10 coins. Later, the innkeeper, in a good mood because his son was born that day, decided to charge only 25 coins and gave the remaining 5 coins to the waiter to return them to the three customers. However, the waiter secretly kept 2 of the coins and gave each customer 1 coin back. That means the three customers each paid 9 coins with a total of 27 coins, right?"

Merlin followed Arkhan's explanation and silently calculated, even though the people of this era generally had low mathematical skills, it was clear that he was an exception, and this was nothing more than a simple addition and subtraction problem.

"Right. So, what's your question?"

Arkhan calmly continued, "They paid 27 coins, plus the 2 coins the waiter kept, which makes it 29. However, they originally took out 30 copper coins for the payment. So, where did the remaining 1 copper coin go?"

"!!!"

Merlin was left dumbfounded in an instant, including Artoria who had been silently calculating on the side.

Merlin subconsciously recalculated it several times, finding that the answer remained the same, a total of 29 coins.

If that was the case, where did the missing coin go?

Cold sweat began to trickle down Merlin's forehead. He never expected the first question posed by his opponent to be so sharp.

He stubbornly recalculated several times, but the answer remained unchanged. The missing copper coin seemed to have grown legs and disappeared.

Watching Arkhan, who had a calm expression, Merlin suddenly had a flash of insight.

If it wasn't a calculation issue, then it was likely... a wording issue!

Using verbal loopholes to set traps for others was his most commonly used trick!

If that was the case...

Merlin closed his eyes, appearing as though he was asleep, but in reality, he was using magecraft to simulate the scenario.

If Arkhan had indeed set a verbal trap for him, he would only fall into a dead end by following his opponent's line of thinking, and he would never find the correct answer.

The only way out was to step out of the verbal trap and speak based on facts!

After a moment, Merlin opened his eyes, wearing a confident smile.

"That 1 coin never existed in the first place. The 9 coins the three people paid already included the 2 coins that the waiter kept, which is the discounted price of 25 copper coins plus the hidden 2 coins on the waiter with a total of 27. Adding the 3 coins returned by the innkeeper makes it a total of 30 coins."

Arkhan raised an eyebrow and nodded, "Correct."

"Hahaha!" Merlin's face displayed a smug expression, and he grinned, "I must admit, your question was indeed cleverly crafted. For an ordinary person, it might be challenging to spot the trap and fall into your snare, trapped in a corner with no way out.

"But unfortunately, you encountered none other than the brilliant, wise, and handsome Merlin, the mastermind of trick and calculation. These small riddles can't possibly stump me, mwahahaha!"

Watching Merlin's overly confident laughter, Artoria furrowed her brow slightly, sensing that his method of winning might not be entirely straightforward...

However, she couldn't say anything because, from the beginning, Arkhan didn't set any specific conditions. As long as Merlin could answer correctly, it would count as a win.

"Next question." Arkhan ignored Merlin's laughter and continued calmly. "Assuming 1 coin can buy 1 peach and 3 peach seeds can be exchanged for 1 peach, you now have 10 coins in your hand. Each peach you eat leaves a seed. How many peaches can you eat?"

Merlin paused for a moment and then laughed even more exaggeratedly, clutching his stomach and tears forming at the corners of his eyes. "You... are you out of tricks? To think you would ask me such a simple question! Or perhaps you realize you can't beat me, so you're giving up?"

Arkhan didn't respond, his black eyes remained calm as he watched Merlin.

"Alright, alright, it looks like you've really run out of tricks. I told you not to challenge the wisdom of a great mage." Merlin wiped away a tear from the corner of his eye, cleared his throat, and said, "Listen up! 10 coins can buy 10 peaches, and with the 10 leftover seeds, you can exchange for 3 more peaches. After eating those, the 3 leftover seeds can get you 1 more peach. So... that makes a total of 14 peaches!"

"Are you sure?" Arkhan asked casually.

"Of course!" Merlin confidently replied. This kind of question could be answered even by a three-year-old child, and he didn't even need to use magecraft to simulate it.

"Your answer... is wrong..." Arkhan said with an unchanged tone. "The correct answer is 15."

"Why!?" Merlin was dumbfounded once again.

"According to your logic, your exchange of the first 3 peaches should only use 9 seeds, leaving 1 seed unused. With 1 more seed from the last peach you exchanged, the seeds became 2. But you can ask for 1 more peach as a debt to be paid later. That way, you'd have 3 seeds again, just enough to exchange for another peach." Arkhan explained casually. "So, it's 15, isn't it?"

"What the?! You... you're twisting words!" Merlin pointed at Arkhan indignantly. "Who in the world exchanges peaches like that!?"

"Is that so? I thought you should be quite familiar with the concept of debt." Arkhan replied nonchalantly.

"Pfttt!" Artoria couldn't help but burst into laughter.

Merlin blushed and protested, "This... this is different! Besides, I've never taken anything in debt. I survive on my charm, I don't need to repay anyone!"

'I've never seen someone justify not paying debts so confidently...' Arkhan's lips twitched.

Filled with regret, Merlin forced a smile and said, "Fine~ fine~ I'll admit defeat this time... but I still have one last chance!"

As long as he could answer this final question correctly, he had a chance to redeem his honor!

Merlin got unusually serious, his eyes burning with the flames of determination.

This was no longer just about winning or losing; it was about his reputation and dignity as a great mage!

Although his reputation wasn't particularly important to him... as the mage responsible for training the king, he couldn't afford to lose in matters of intellect!

Let the final showdown begin!

"The third question..." Arkhan paused for a moment but then he smiled with a hint of mischief as he watched Merlin's eager eyes.

Merlin furrowed his brow slightly, for some reason, when Arkhan smiled like that, he had a bad feeling.

"The third question—divide a map into non-overlapping regions, label each region with a number, what's the minimum number of different labels needed to ensure that no adjacent regions share the same label?" Arkhan said leisurely.

Merlin's mind spun for a while, and when he finally understood the meaning of the question, he became utterly confused.

'Label regions with numbers, and ask for the minimum number of labels to ensure no adjacent regions share the same label... What kind of complex question is this?'

Merlin frantically simulated it with magecraft in his mind, but after trying for a while, he realized it was impossible to simulate this!

The possibilities were simply too numerous!

Artoria, beside him, frowned deeply. She didn't attempt to solve the problem like Merlin because her intuition told her that this seemingly simple question might not be solvable by human effort.

The Four Color Theorem, also known as the Four Color Map Theorem, was one of the three major unsolved mathematical problems of the modern era, alongside Fermat's Last Theorem and the Goldbach Conjecture. It was proposed by a British student, Francis Guthrie, in 1852, and it wasn't proven until 1976.

This problem seemed deceptively simple, but it had profound implications. To prove this conjecture, the University of Illinois used two electronic computers, spent 1200 hours, and made 10 billion judgments.

Staring at Merlin, who was dripping with sweat, Arkhan crossed his arms and remained remarkably composed.

'No way you can solve this. If you solve this problem, I'll immediately return to the Land of Shadows, and I won't come out again!' Arkhan thought with a sneer.

"I... I think it's eight..." Facing Arkhan's gaze, Merlin could only reluctantly spit out a number.

"Wrong. The correct answer is four." Arkhan said calmly.

"Why!?" Merlin asked, refusing to accept it.

"Well... this question is a bit tricky to answer, and you might not even understand it..." Arkhan said nonchalantly. "If you think it's incorrect, you can try to provide a counterexample, although it's unlikely."

What a joke, Arkhan could remember the formation of the Mandarin Duck Formation, but there was no way he could remember the proof of the Four Color Theorem.

Moreover, that kind of problem was practically unsolvable by human effort.

Merlin reluctantly attempted to solve it with magecraft, but after a whole hour, he couldn't find a counterexample.

'Could it be... the answer really is 4?'

With trembling eyes, Merlin looked at Arkhan, feeling the overwhelming superiority from the realm of higher intelligence.

He tilted his head down, his eyes vacant, his expression lifeless, as if he had turned into a gray photograph.

"It seems the result is quite clear now..." Arkhan said, looking at Merlin as though he had turned into stone. "I'm sorry, Merlin, but you've lost this second round."