Chapter 5: 5- Problem

A grey mist enveloped Han Lingyun as he placed his hands flat on the mirror. Then the mist started to converge into a gentle stream of condensed gas slowly circling around him. After a short moment, a second stream appeared circling around him, on the opposite side of the first one, like yin and yang. As the second stream appeared it reinforced the first and they both appeared twice as dense as previously. Then a third stream appeared, and the 3 streams formed the pattern of a rotating triangle. The 3 streams where now 3 times denser than the original stream. And again, another stream appeared, framing Han Lingyun in a rotating square.

Han Lingyun was mesmerized as he looked at the whole process. Each additional stream seemed to complete a whole. After the 4th one, each stream was 4 times denser than his first stream. Those patterns remained grey all along. He raised his head full of expectation as the mist around him started to dissipate.

"Very well, grade 4 talent, no particular affinity." An elder nodded.

Han Lingyun left relieved and couldn't hide his smile once again. This gained him many sideways looks from the other candidates. After escaping his little reverie, he reined it in and waited for the next test.

…

"This test is simple, punch this wall with all your strength, then kick with all your strength." Another elder gave instructions. This particular wall behaved very strangely. If left untouched, it seemed solid but when someone punched or kicked it, it would bend and deform, absorbing the shock and making sure that the candidates were not hurting themselves. Two Elders were again recording the results.

…

"Sprint as fast as possible to this 50m line!"

…

"Do pushups until you can't!"

…

"Finish this Sudoku as quickly as possible without mistakes!"

…

"You have 9 crystals. They all weigh the same, except one which is lighter. You have a double pan balance scale. You can perform a maximum of 2 weightings to find the different one. Can you do it and how?" a middle-aged looking man questioned with a gentle smile.

Han Lingyun thought for a moment and found the solution.

"Simple, you make 3 groups of 3 crystals. Then weigh 2 groups of 3 crystals, one group on each side of the scale. If they have the same weight, that means the lighter is one of the 3 remaining crystals. If one group is lighter, the lighter crystal is in it. Now you have 3 crystals remaining and you do the same thing: one crystal on each side of the scale: if one is lighter that's the different one, if not, the different one is the remaining crystal." Han Lingyun proudly gave the answer.

He loved those logical problems, and the Elder assessing him kept giving him more complex ones, to the point where the man didn't know what problem to give Han Lingyun. Feeling numb, he decided to try to find something that he knew Han Lingyun couldn't answer to curb a bit his enthusiasm: "Tell me young man, what is the year on the Sun' Empire calendar?"

"It is the year 513 Elder" Han Lingyun dutifully answered.

 

"Very well.

Mr. Han is a cultivator with a pile of 513 crystals. He takes out a crystal from the pile, which is now left with 512 crystals. Mr. Han has a double pan balance scale and he decides to put 256 crystals on each side. He finds out that the two sides balance each other out: they weigh the same. Mr. Han bunches back up the 513 crystals together and starts again by putting away a new crystal and weighing two piles of 256 crystals. He reenacts the same experiment for all of the 513 crystals. Every time, he finds that the two remaining piles of 256 crystals weigh the same.

The question is, can Mr. Han deduce from that experiment that all the crystals have the same mass? If so, how do you prove it?" the elder asked, having fun by stunning this smart brat.

 

Han Lingyun thought for a moment with a frown. With a teasing smile the elder added: "You can give me an answer after the group finishes passing this test if you find anything useful. Remember, all the crystals might have completely different masses."

As the tests were going on, Han Lingyun sat down with a dazed look. 'The answer is obvious when we suppose that there are only 1 2 or 3 stones with different masses, it doesn't work. The question is how to generalize this? Hum, this elder is obviously trying to trap me by giving me a problem that sounds easier than it actually is. Let's look at this with a different point of view, I might as well try to formalize the problem.

Han Lingyun approached the Elder that had been assigned to the G group all day. "Excuse me Elder, can I have a pen and a paper? The Elder inside gave me a hard problem to think about and I need to do some reasoning." The middle-aged man leading the group suspiciously looked at Han Lingyun but still acquiesced without raising another question and took out a message talisman. He sent it after speaking a couple of words. One minute later a disciple dropped the paper and plume with ink which Han Lingyun quickly caught.

'Hum, I also have math tools at my disposal to solve this sort of thing. I can think about this problem by looking at the vector of the weights. Then I have to analyze matrixes with the same number of 1s and -1s on each line with 0s on the diagonal….'

Han Lingyun began to plunge into the problem as other disciples took turns to enter the tent and try to solve these logic problems.

 

…

 

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Yun San was a kid from a prominent town of the region. Being a member of the prominent Yun family, he already had a physical and martial arts education, but also special teachers for music poetry history and more. However, he was currently completely stumped: 'What is this stupid question? There is no way you could find the light stone with only 2 weightings!' As he struggled to find an answer, the elder was counting seconds in his head as the awkward moment stretched on. Suddenly another child barged in the tent.

"ELDER, I FOUND THE ANSWER! They all have the same weight, here!"

Both the Elder and the disciple taking the test were dazed by the sudden entrance. Han Lingyun however was only thinking about the problem and handed his answer. The elder quickly grabbed the paper and skimmed through the content, before putting it to the side. He raised his head with a rare look of appreciation, and a slight disbelief. "Young man congratulation, your proof is valid. How do you know so much?" Only for Han Lingyun to respond all smiles: "My dad taught me; he is a professor at the capital."

"Well young man, I must say that you surprised me on this one, actually I wasn't even expecting an answer. By the way, you can call me Elder Wen."

Meanwhile, Yun San, still dazed, was looking incredulously at all this. Then he felt humiliated, they acted as if he was invisible. Humiliation turned into anger. When was he even disregarded like this, a member of the Yun clan? He just walked away fuming. The elder seemed to recall that someone else was here, but was not impressed by the candidate storming off.

"Oh, another arrogant brat who hasn't come back to earth after a lifetime of pampering and privilege. We don't need any of that crap in the sect. All right Mr. Han Lingyun, you should catch your group for the next tests. Remember in the future if you need anything, you can ask for elder Wen, I should be at the Array Pavilion. I could also give you some nice little problems if you want." Elder Wen added.

"Thank you, Elder Wen, I will make sure to do so." Han Lingyun didn't hide his excitement and appreciation.

Nothing stoked him more than a good old little problem. In addition, Han Lingyun was very excited to discover that he wasn't the only one with an interest in math in the sect.

…

The tests continued on. This time all the group was taking it at the same time "Stay in this uncomfortable position for as long as possible". Han Lingyun, knees bent, arms straight ahead, was clearly uncomfortable here, in fact he ended up abandoning in the middle of the pack. The elder looked sternly at the group, a strong Dao heart is greatly valued, those who persevere longer even as they are suffering will be greatly rewarded in the rankings. Han Lingyun could only scratch his head; pain tolerance wasn't really his thing.

Finally, it was time for the final test, perhaps the most unexpected one.

"Tell me in your own words, why do you wish to cultivate?" a stern looking old woman asked.

"I want to understand the world better, I want to answer its mysteries, I wish to escape the shackles of the mortal body to peer into the heavens. For all this, I need to reach a higher realm."

"Hum all right…" the elderly woman didn't seem convinced.

 

At last, the 4176 young candidates were grouped at the center plaza for the announcement of the final rankings.

"Here are the rankings for the entrance in the sect. No complaints, everything is factored in, even what you did when you were not taking a test."

A murmur ran through the crowd. An elderly and feeble-looking man waved his hand and a huge tablet appeared with 800 lines.

Han Lingyun quickly started to search for his name before letting out a breath of relief: he was ranked 16th! Around him, more and more kids started to cry in joy as they finally saw their name. Others became more and more frantic as they desperately searched for their name without success.

Han Lingyun was already analyzing the significance of his rank. 'I guess my 4th grade talent and my excellent logic test results have played a crucial role in my score, because my physical capabilities are clearly inferior to those that have already followed some kind of training. I wonder how many have 4th grade talent, I should probably ask the elders.'

The elderly man continued: "Those who have their name on the tablet, step to the right. Others, to the left." As the group separated in two, many started to tear up. It was a difficult disillusion for many children, being rejected after dreaming of the cultivation life and being tested with a spirit root.

The frail looking old man turned towards the rejects. "You can still start on the road of cultivation. In fact, after reaching the gate, karma has already linked you to the cultivation world. The sect masters of our subsidiary sects will come to pick you up and divide you lot among themselves. This arrangement is probably beneficial for all of you too, it is better to be the head of the rooster than the tail of the phoenix. As for the 800 selected, come with me get your accommodation, tomorrow you will meet the previous generation of disciples."

The group was bubbling with excitement, finally they passed their first hurdle, this time they truly embarked on the long journey of cultivation.

 

 

 

***

For the true elite that want Han Lingyun's detailed proof for the 513 crystal problem, here is a retranscription of his written solution. :)

https://docdro.id/VKnXSPL

(You DON'T need this to follow the story, it's just for those interested in the math aspect.)

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