Magus Tech

A two-minute game, which lasted for a long time, until the sun on the west side mostly settled down, leaving only a red edge glowing, pulling the shadow of the chess pieces on the board.

"Snapped!"

Richard once again fell, and the clown swept the board and saw the problem. He said bluntly: "I lost again, but it doesn't matter, we will come again! I don't believe it, I can't win a game." Pack up the chessboard and pick up all the white pieces.

Richard, however, refused aloud: "No need for Mr. Clown. Even if you play another one hundred games, as long as I take the black spots first, you will definitely lose. This has nothing to do with chess and mathematics. It is calculated."

"Huh?" The clown stopped picking Bai Zi, looked at Richard, and asked aloud, "What do you mean?"

"I mean, although the rules of Gobang are simple, there are loopholes after calculation. Without any restrictions, the first move of the blacks is a win, yes, a win-as long as you go in a specific way, and any Everyone wins.

Generally speaking, in order to be fair, the normal game will have'three and three prohibited hands','four and four prohibited hands','four and three prohibited hands','four and four prohibited hands', and'long continuous prohibited hands' .

The so-called'three-three banned hands' means that Kuroko will drop one son and form two or more triplets at the same time. This is the premise that Baizi can't resist at first.

Therefore, in a normal game, Kuroko will be negative if he gets out of the'three-three forbidden hands' or is forced to get out of the'three-three forbidden hands'.But now there is no forbidden hand in the match between us, then you naturally have no hope of winning."

"Can this be calculated?" The clown was still a little unconvinced.

"In fact, the simpler the game, the easier it is to calculate." Richard said, "If you have doubts, we can play another game."

"what?"

"Game with chess pieces." Richard said, taking the chessboard away, grabbed a piece of chess, counted a total of nineteen pieces, and divided them into three piles.

There are three pieces in the first pile, seven pieces in the second pile, and nine pieces in the third pile.

"The rules are like this," Richard said. "The two of us take turns to take pieces from these three piles, and each time we can choose any pile. The number of pieces taken is at least one, and at most one pile is taken away. Wait until the last piece left is taken, whoever loses."

After a pause, Richard looked at the clown and continued: "This game is not the same as backgammon, but it can also be calculated by mathematics, so the first move is also a win."

The clown's eyes flickered, staring at the pieces for a long while: "I don't believe it, I now think of several ways to win backhand."

"In this case, let's try it." Richard said, taking the first five from the pile of the nine rightmost pawns.Three piles of chess pieces immediately turned into "Three Seven Five".

The clown thought about taking the remaining four chess pieces on the far right, and turned into a "Three Seven".

Richard then took the second pile of four pieces and turned into a "three threes".

The clown stared at the chess pieces for a long time, but did not start. He looked at Richard and asked, "Am I losing now?"

"Yes." Richard nodded. "Although there is no result yet, you have lost.

Now it's 3:3. If you take one pile at a time, I can take two of the remaining pile and leave one for you. You lose.If you take two of the pile, I take the other pile and leave one for you, you lose.

Out of caution, if you take only one pawn from one pile, then I will also take one pawn from the other pile and become 2:2.

And 2:2 and 3:3, there is no essential difference-you take a pile, I take another pile of one, leave you one, you lose.You take one of the piles, and I take all the other piles, leaving one for you, you still lose.No solution."

"But this is only one situation, and there are other situations. It is impossible to win because you are the first to do it," the clown insisted.

Richard shakes his head: "It's really not just this situation. The overall situation can be roughly divided into three types, that is, the evolution to the end, and the winning form left by the first move.

The first form, the most extreme, leaves you with a pile and only one piece.Whether you take it or not, you lose.

The second form gives you two piles, as long as the number of the two piles is the same, no matter how many, the final form will become 2:2, or the first form, you lose.

The third form, the remaining three piles, is more complicated, but it will eventually become a little bit of the first two, as long as you do not make mistakes in the first move, you still lose in the second move."

"But how can you not make mistakes first?" The clown's voice grew louder and slightly disorientated, "You don't know how I think, how can I control my way of taking? And since you can't control my way of taking, how? Can you guarantee that you won’t go wrong every time you take it?

"It's not that complicated," Richard said. "In the calculation, I don't need to know how you take it, just give you an equilibrium state. To put it simply, first, I convert the number of pieces in each pile into binary. Horizontal arrangement. By the way, binary is to change the ordinary calculation of "every ten in one" into "every two in one", like this."

Richard said, using a slender piece, write three lines of numbers on the ground:

0011 (3)

0111 (7)

1001 (9)

Then draw a horizontal line under the three lines of numbers, and add the numbers under the horizontal lines to become numbers:

1123

"With such a definition, a number that is a multiple of 2 is an even number, otherwise it is an odd number. Among the four numbers of 1123, there is an odd number, which is a non-equilibrium state.

And all I have to do is to get you a balanced state by taking pieces, for example, at the beginning I took five from the third pile and became a balanced state, which is how it is."

Speaking, Li Cha erased the numbers he wrote, and wrote them again with slender pieces:

0011 (3)

0111 (7)

0100 (4)

——

0222

"Now all numbers are even, which is an equilibrium state. In the equilibrium state, no matter how you take it, all I do is continue to change it back to the equilibrium state, so that in the end, you lose.

So, it doesn't matter how you take it, as long as I start first and come up with a balance, you lose.This is the reason why the first move must win-it is not me who beat you, but mathematics, binary.

This is simpler than the principle of Gobang and requires less calculation. You should be able to figure it out."

When Richard finished, the clown was silent.

The clown in silence, staring at the numbers written by Richard for a long time, and then he started to write on the ground with his pieces, and then divided three piles of pieces to simulate continuously.The result of the simulation is the same as what Richard said-every time you win first.

Eventually the clown looked at Richard, his expression very complicated.

Richard said: "Mr. Clown, you see it. It's hard for me to play'Clown Chess' with you, but if you play games like "Gobang" and "Take Chess" with you, you will always You can’t win. The reason for this is nothing to do with wisdom and humility, it’s just a matter of choice.

The reason why you choose to play'Clown Chess' with me is because you know that you will win before you play.And I also know that I will win if you play "Gobang" or "Take Chess Pieces" with you.This is caused by differences in areas of expertise, and can also be seen as differences at home.That's why I don't agree with what you said at the beginning."

"Right." Richard looked at the clown and asked seriously, "In other words, Mr. Clown, do you remember what you said to me, right?"

"I--" The clown stood up and looked at Richard, his eyes changed several times in a row, and finally took a deep breath, suddenly turned around, "The wooden platform is built, I should perform, the game will end first, there is Opportunity... Let's talk next time."

"Is there another time?" Richard asked.

"Maybe." said the clown, and walked toward the wooden platform without looking back.

At this time, the sun in the west was completely set, the sky followed a black, Li Cha looked at the back of the clown, his eyes narrowed.

...