Mathemagical Card Trick

How to perform a common magic trick whether you're a magician or a mathematician.

Ask a friend to randomly select a card from a deck of 21 cards. Have them memorize this card and return it to the deck without revealing it to you.
Optional: Have them shuffle the deck themselves!

Start by creating three columns of 7 cards each by:
First, lay the top 3 cards in a row from left to right. (picture 1)
Then add a second row on top the first . (picture 2)
Continue adding rows in this manner until each column has 7 cards. (picture 3)

Have the friend select which column their card is in.
Without changing the order of the cards in this column, gather it into your hand face down, followed by the other two columns on top.
Note: The order of cards in the other two columns no longer matters.

Repeat Steps 2 and 3 beginning with cards from the top.
Repeat a third time.
After the third time doing this process the card your friend selected will be the last card in the column they chose.
Memorize this card!

Randomly shuffle the cards into a deck. Begin flipping cards over one by one face up until your friend's selected card is revealed. Impress them with your mathemagical knowledge by identifying the card.