Explanation of an Amazing Mathematics based Card Trick

Published by Ganit Charcha | Category - Math Articles | 2022-02-18 03:37:18

Assumption – We assign value $1$ to Ace, and Jack (J), Queen (Q) and King (K) all are assigned value $10$.

The magic goes as follows.
Step 1 – Pile $26$ cards (from a deck of $52$ cards) one after another in face up condition.
Step 2 – Place this deck of $26$ cards below the other deck of $26$ cards to make again a pile of $52$ cards.
Step 3 – Now from top take out three cards and place them in face up condition.
Step 4 – For each face up cards, we take out cards from the deck to make a pile until we get $10$, starting from the number either written or assigned to the face up card.
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.
Step 5 – Add the numbers written or assigned to the first three face up cards in Step 3. If $N$ is the result
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.
Why this trick works?
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
$$3 + (10 -x) + (10 – y) + (10 -z) = 33 – (x + y + z),$$
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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