The magic goes as follows.

For example, if 3 is written in the card, we take out $7$ cards one after another as that makes it count

$4, 5, 6, 7, 8, 9, 10$. If $10$ is already the assigned number of the card, we then do not take out any card.

of addition, then magician can predict the $N$-th card from the remaining deck of cards.

To understand the steps of the Magic better, look into the YouTube video below.

How magician predicts this?

In Step 1, while piling up the $26$ cards in face up condition, magician needs to take note of the $7$-th card.

The $N$-th card, at Step 5, which magician is predicting, is the $7$-th cards which he/she has taken a note of in Step 1.

Note and convince yourself that the $7$-th card which magician has remembered (or taken a note of), after

Step 2 is the $33$-rd card from top (in the deck of $52$ cards).

In Step 3, we are taking out $3$ cards and placing them on the table in face up condition. Let, the numbers

in these three cards be $x$, $y$, $z$, where $1 \leq x, y, z, \leq 10$.

[Remember, Jack (J), Queen (Q) and King (K) have all values equal to 10.]

In next step, we are counting from $x$, $y$ and $z$ upto $10$, to add $(10 -x)$, $(10-y)$ and $(10-z)$ number of cards respectively to make 3 piles.

Therefore, after step 4, we have taken out

$$3 + (10 -x) + (10 – y) + (10 -z) = 33 – (x + y + z),$$

$$3 + (10 -x) + (10 – y) + (10 -z) = 33 – (x + y + z),$$

number of cards from the top of the deck of cards.

At step 5, from the remaining deck of cards, magician is predicting the $(x + y +z)$-th card,

which is nothing but the $33$-rd card from top after step 2. And this card magician has already taken a note

of in step 1.

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