尤も、此度は誰もが気楽に楽しめるよう、高校数学の一端をパズルゲームとして捉えつつ、暫定的にかつ部分的にざーーっと記してみた。
だから本問は淡泊なコンテンツに如かず、しかも設問も簡単で、だからおそらく先般のものよりは易しいはずである。
（本稿はすべて僕自身の作成であり、文責は僕個人に帰属する。）
えっ？ なんだって？
なぜおまえごときがこんなふうな英文解釈課題を自前で起こすのかって？
大抵の高校英語教材が陳腐で退屈なものばかりであり、学際的な思考の楽しさをほとんど喚起していないからだよ。
Read this following text from paragraph [1] through [3], then answer the accompanying <Questions> hereunder.
Number of Cases
[1] Wherever the probabilities of certain events' occurrences are required in % scale description, the most basic stage before detailed calculation must be maximum-minimum counting of those cases. And it is normally done with the 'case counting' methods in mathematics.
Let's pay a little glance to some aspects of case counting math. Do not worry. This text just presents funs and thrills of high school math puzzles.
Yet, some features of case counting may go beyond your daily perspectives.
===================
[2] Challenge our daily senses of scales.
Do you play cards (※1) ? Most of you do.
Suppose you have just 3 different cards as of 💛J, 💛Q, and 💛K. Then, when you put each of them in one straight line, how many different cases can you make ?
Of course, by adopting our basic case counting formula, we can automatically find out the number of cases as of 3! = 3x2x1 = 6.
All right. Then what about 💛10, 💛J, 💛Q, 💛K and 💛A ?
Similarly, the number of cases is 5! = 5x4x3x2x1 =120. Easy, so easy.
Then, what if you are responsible with the total 52 cards, complete them in one straight line ?
52! is the instant answer, why not ?
But, how large is this ? It's 52x51x50x49x48x47x46x45x44x43 ... .
This is where you must abandon your common perspectives. The number of these possible cases astonishingly reaches up to 68 digits, cruelly bursting out your daily calculator and defying your high-end computer programmes.
If (a big if) you take 1 second per 1 case counting, the total time necessary for the full 52! cases is unimaginably far huger than that so far spent since the generation of the universe.
Who has ever tested this ? Can't you believe me joking that some cases within were once coded by devil ?
=================
[3] Join a smart trick with temporary symbols.
Suppose you have 6 tennis balls, and all these 6 balls cannot be identified individually.
Now. you must deliver all these 6 balls to 4 different persons - identifiable as A, B, C and D. The number of balls per your delivery can vary from null (0) to 6, not exceeding 6 in total.
Case example [1]: 1 ball to A, 2 balls to B, 2 balls to C, 1 ball to D
Case example [2]: 3 balls to A, 1 ball to B, 1 ball to C, 1 ball to D
Case example [3]: 1 ball to A, null(0) to B, 4 balls to C and 1 ball to D
... .
Then, how many cases can you have in ball deliveries to these receivers ?
Yes, this is a textbook math, but, remember that the premise here shall include the possible cases of null(0) delivery to any receivers. So, we cannot simply apply the elementary combination formula (leading to 6C4).
Now, a classic solution herein is to add 3 same 'temporary separators' as of the symbol "│", and let them stand among each receiver. In each case, we must count the numbers of balls and 'temporary separators', equivalently combined, while ignoring any null(0) cases.
Let's confirm if this trick really works, adjusting it to the two examples shown above;
Case example [1]: ●│●●│●●│●
Case example [2]: ●●●│●│●│●
Case example [3]: ●│null│●●●●│●
... .
Accordingly, the total number of ball delivery cases must be 9C3 = 84.
All right. This operational trick is practically devised in many computer algorithms as well as in object-counting machines.
And, in farther broader terms, we can say this is how some mathematical tricks have re-invented physics since the dawn of our civilization.
===================
(※1) トランプカードで遊ぶ
==============================================
<Questions>
[Q1]. In the paragraph [1], why can we say that some features of case counting may go beyond your daily perspectives ?
(1) Because some of those methods are not common to all people over the world
(2) Because some of those calculations betray human's common imagination
(3) Because some of their tricks are theoretically wrong
(4) Because some people will argue the preciseness of case counting math
==================
[Q2]. In the paragraph [2], what can be our daily senses of scale ?
(1) Our counting ability of natural numbers
(2) Our prospects to future events
(3) Our confidence in our own natural senses of scales
(4) Our belief that we understand all sorts of math outputs
=================
[Q3]. In the paragraph [2], what is the bottom line of the author's joking (that some cases were once coded by devil ?)
(1) Lining up the cards in all 52! cases will be almost impossible to anybody
(2) Lining up the cards in all 52! cases will be possible to somebody but you
(3) 52! is an imaginary number
(4) Nobody will be happy in calculating the number 52!
================
[Q4]. What can be the main lesson we learn from the temporary symbol trick shown in the paragraph [3] ?
(1) Case counting shall not consider null (0) occurrence
(2) That trick puzzle is not suitable to math education
(3) The formula of combination is imperfect in itself
(4) Temporary symbols can be counted for its quantities
===============
[Q5]. In the paragraph [3], what does the author imply by saying that some mathematical tricks have re-invented physics since the dawn of our civilization
?
(1) Mathematics can deliver just logical symbols to overcome some physical limitations in materials
(2) Mathematics has always been recorded in books since the first day of mankind, while physics has not
(3) Mathematics has always distorted the laws of physics since the generation of universe
(4) Mathematics is insincere in itself against human and has spoiled our technologies and industries
==============
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