Published by Ganit Charcha
| Category - Math Articles | 2025-06-07 08:56:18
In this article, we will describe the Mathematics behind the amazing card trick – “The Final 3”.
The steps of the Magic goes as follows.
Step 1 – Magician will ask the subject to secretly choose 3 cards and keep it with him or her.
Step 2 – Magician then shuffles the card and makes three pile of cards with 10, 15 and 15 cards respectively in each pile in face down condition. Magician is left with 9 cards in his hand and that makes the 4-th pile.
Step 3 – One of the secret card, magician then asks to place on the top of the pile with 10 cards in face down condition. Magician then takes out randomly any number of cards from the top of the second pile of 15 cards and puts it on top of the secret card.
Step 4 – Place the second secret card as face down on top of the remaining cards of the second pile. Magician then takes out any number of cards from the third pile containing 15 cards and puts it on top of this second secret card all in face down. Now put this pile of cards on top of the first pile of cards at the end of Step 3.
Step 5- The third secret card will finally be placed in face down on top of the remaining set of cards of third pile. All the 9 cards from the 4-th pile, magician then places on top of this third secret card. Magician then places this pile of cards containing the third secret card on top of the pile of cards at the end of Step 4.
Magician is now having a single pile of 52 cards without having any idea of which three cards are secretly chosen. He is also not having any idea of what cards are on top or bottom of those three secret cards, because all the above steps are carried out with cards being in face down condition. We will see next, how Magician can figure out all the three secret cards by carrying out some steps.
Step 6 – Magician then starts to place the cards alternatively in face up and face down condition. So, first card from top will be placed in face up, second card in face down condition, third card in face up condition and fourth card in face down condition and so on. Magician then gets it ascertained from the subject that none of the 3 secret cards are amongst the 26 cards which are in face up condition.
Step 7 – Magician then takes out the pile of 26 cards which are in face down condition and repeats Step 6 in exactly the same way. Magician then gets it ascertained that none of the 3 secret cards are amongst the 13 cards which are in face up condition.
Step 8 – Magician now takes up the pile of 13 cards which are in face down condition and alternatively will place the cards in face down and face up condition. So, first card from top will be placed face down, second card as face up, third card as face down and so on. Unlike the Step 6 and Step 7, here first card goes as in face down condition. Magician gets it bounced from the subject that none of the three secret cards are amongst the 6 cards which are in face up condition now.
Step 9 – Magician then picks up the 7 cards which are in face down condition and repeats the Step 6 in exact similar way. At the end, Magician is left with only 3 cards in face down condition and these 3 cards are the ones secretly chosen at Step 1. So, The Final 3 cards are the ones secretly chosen.
Why this card trick works?
Note and make yourself convinced that, at the end of Step 5, from the top of the pile of 52 cards, 10th, 26th, and 42nd cards are the chosen secret cards.
In Step 6, since we are placing alternatively the cards in face up and face down condition, so 1st, 3rd, 5th, 7th and so on are the cards which are in face up condition, whereas 2nd, 4th, 6th, 8th and so on are the cards which will be in face down condition. Therefore, all the 3 secret cards are in the second set of cards which are in face down condition.
So, at the end of Step 6, from the bottom of the pile of 26 cards which are in face down condition, the secret cards are in 5th, 13th and 21st position. That means from the top of the pile, secret cards are in 6th, 14th and 22nd position.
Magician then repeats the same procedure at Step 7. So, from the bottom of the pile of 13 face down cards, secret cards are in positions 3rd, 7th and in 11th position. That means from the top of the pile of 13 cards, the secret cards are in 3rd, 7th and 11th positions.
In Step 8, Magician puts this pile of 13 cards with first card being in face down, second card being in face up and 3rd card being in face down condition and so on. Therefore, secret cards now come in the pile of 7 face down cards with their respective positions being 2nd, 4th and 6th from top of the pile.
At the end of Step 9, Magician repeats the same procedure as Step 6 and gets only 3 cards in face down condition and these final 3 cards are the ones secretly chosen. So, Magician can successfully figure out all the 3 secretly chosen cards.
