Name: 中国語の余弦定理とカード - Numberphile (Chinese Remainder Theorem and Cards - Numberphile)
Uploaded: 2021-01-14T10:42:07.000Z
Duration: 11 min 13 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

Two sets of cards, 1 2 3 4, ace is one, 4 3 2 1, again ace is one,

spades and hearts, black and red. They're in opposite orders. I now turn them over

we're going to shuffle them and you decide which one to shuffle but the shuffling means always to take the top card and

And, each time we shuffle, you tell me which one to shuffle, I'll shuffle that one.

Okay, so let's shuffle a number of times. Well, what can we say? Oh, let's use the phrase numberphile shall we?

So, for each of these letters you say well, shuffle the right one or the left one. And you can say

You can choose whatever you like. Okay, so Brady, you tell me which one to shuffle, then.  So left or right?

Okay, so those two cards emerged to the top as a result of your choice, I didn't choose this.

So I'm going to set them aside. Yeah, two of them.

Now, we repeat numberphile again and for each of those letters

We shuffle either of these and you choose which ones shuffle for each of those data. So which one do you want?

Let's do . . . Let's do all of them that one.

I wasn't expecting this. Okay those two cards emerged to top.

In fact, this one didn't move but this emerged to the top so I put these aside.

Now one last time, numberphile, and you choose which one to shuffle.

Now if we were really lucky and luck doesn't come except to the deserving.

Because numberphile is such a magic phrase,

You know numberphile means "liking numbers" and these two numbers like each other, of course, 2 and 2, but that might have been luck.

But if we really believe in that magical numberphile, these two might have matched

Remember, you chose which one to shuffle, yeah?  I didn't.  That's surely not possible.

But what's really impossible would be impossible?

Is for the next two to match and the surprise par surprise, the last two also match.

Lovely!  Numberphile -- I knew it was magic.

So the trick that I have just shown you is a classic trick which was described for the first time as far as I know

by the late Martin Gardner called The Last Cards Match

and I made a variation on this and the variation is a little slower than the original trick

But it's also mathematically more interesting. So I'd like to reveal the secret.

Or if you like 4 3 2 1 in the reverse order, and these should be thought of as like clocks

Okay, so a clock has you know, 1, 2, 3, 4 all the way to 12 and then it starts all over again.

Also, if you go one two, three four, and if you want to go five here six here seven here eight here

And so we can keep going. Okay, you remember that our way of shuffling was very special

We took the top card and then put it at the bottom

So you . . . as you keep repeating this you are cyclically or cyclically depending on the side of the Atlantic

Permuting those cards so you go from here to here to here to here and keep going

Whereas in the other deck which had the reverse order you go from to here to here to here, okay?

We had four cars but let's generalize and explain a little bit because this card trick works with any number of cards in general.

Let's say that you have cards one two three and so on

Arranged in a cyclic fashion all the way to M

M minus 1.  M is number . . . total number of cards and I choose that M for a purpose on the other side you have because

In the reverse order M, M minus 1, M minus 2 and dotto dotto

You keep going and then 3 2 1 you come back like that. OK?

So in our card trick M was four, but in general it works and one shuffle does this:

2 goes to 3 and here you go from M to M minus 1 and M minus 1 to M minus 2 and that kind of thing.

Suppose that on the left, that is the red pile you made

On the right you made R shuffles, L as in left, R as in right.

Well, the total number of shuffles that we made was the number of letters in "numberphile"

11 letters. So we know that L plus R was 11 for us.

So L and R are not independent.  If you chose to shuffle the red deck L times,

automatically you are shuffling, whatever you else you do, the right deck R times, but R equals 11 minus L.

And if you choose to shuffle the right deck, that is the black deck, R times,

you cannot help shuffling the left deck, that is the red deck, 11 minus R times. So you have that relationship.

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中国語の余弦定理とカード - Numberphile (Chinese Remainder Theorem and Cards - Numberphile)

equivalent

phrase

reveal

deserve