Stacked Against the OddsPuzzle #027You are playing a casual game of Standard against your longtime r

Stacked Against the Odds
Puzzle #027

You are playing a casual game of Standard against your longtime rival and infamous rule-breaker: Natasha von Cheat. At the beginning of the game, Natasha pile shuffles her deck four times, and then presents it to you to cut. You try to explain to her that pile shuffling is not a sufficient form of shuffling by itself, and you ask if she could shuffle it again.

Natasha laughs and says: “Don’t be ridiculous! If pile shuffling didn’t randomize the deck, then they wouldn’t call it pile shuffling, dummy!”

You highly suspect that Natasha is trying to stack her deck, but she assures you that there’s no way that she can do that if she pile shuffles her deck multiple times. Looks like you’re going to have to prove her wrong!

If Emrakul, the Promised End was the 47th card in her library before she began shuffling, where should you cut her deck so that Emrakul will be on top of her library? For reference, here’s how Natasha pile shuffles:

1. Natasha divides her deck into five piles: A, B, C, D, and E. To do this, she places the top card of her library on pile A, then the next card on pile B, then C, then D, then E, then back to A. She does this until all her cards are divided into the five piles.
2. After her entire deck is divided, she puts it back together by placing the cards in pile A on top of pile B, then places A and B on pile C, and so on. Pile A will be on top of the deck and pile E on the bottom.
3. She repeats steps 1 and 2 a total of four times for her four pile shuffles.

Think you’ve solved it? The solution can be found here!