Math Delights

from www.youtube.com/watch?v=oLjEulT6ssM
instructions by Nancy Blachman, MathDelights.org

Below is a description of how to perform this seemingly amazing math card trick, which is available online at www.youtube.com/watch?v=oLjEulT6ssM

1. Have a volunteer select 3 cards from the deck and write what they are on a piece of paper (to help you remember them).
2. Next create 3 piles of cards. Place 10 cards in the first pile, 15 cards in the second pile, 15 cards in the third pile; there will be will be 9 cards remaining, but don.t reveal to the spectators the number of cards in each pile or the number of cards that remain.
3. Shuffle the 3 cards that the volunteer selected (in step 1). Place one of the cards on top of the pile with 10 cards; cut pile* #2 (one of the piles with 15 cards), anywhere you want, and then place card #2 on top of the pile; cut pile #3 anywhere you want, and place card #3 on top of pile #3.
   *Definition: Cutting a pile by removing some cards from the top of the pile.
4. Place the 9 remaining cards (described in step 2) on top of pile #3.
5. Place pile #3 on top of pile #2, and then place that pile on top of pile #1.
6. Take 4 cards from the top of the stack and place them on the bottom of the stack.
7. Deal out the cards from the top of the stack, alternating between the two stacks; make sure to place the cards in the first stack face up and the cards the in the second stack face down.
8. Tell any spectator to stop the trick if any one of the selected cards (from step 1) appears in the pile with cards that face up. (None of the selected cards will be face up.)
9. Put the cards that are face up off to the side; go back to step 6, using the stack of cards that were face down, until only 3 cards remain.
10. Flip over the 3 cards; they are the cards that a volunteer selected in step 1.

How does the Amazing Math Card Trick work?