Here at PopMech, we love mind-bending math and logic puzzles, which is why we regularly recruit the sharpest minds in the world to concoct riddles that will test your critical thinking, mathematics, and logic skills. The following riddle is one particularly punishing problem—so go grab a pencil and a piece of scratch paper and prepare to rip your hair out (in the best way). No cheating!
➡ The Problem
All 13 hearts in a deck of cards are arranged in a face-down stack. You pick up the stack and begin to deal them out in a curious way: You take the top card and move it to the bottom of the stack, then, you take the new top card and lay it face up on the table. You continue this sequence of two moves until you place all 13 cards face up on the table.
In order to lay out the cards face up in perfect numerical order—2, then 3, then 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace—how must the stack of cards be arranged in the first place?
➡ The Solution
Play this in reverse. Take all the hearts from a deck of cards and lay them out in numerical order from 2 up to Ace. From there, think about where the card will need to go in reverse.
To start, pick up the Ace and put it face down in your hand. Then, put the King on top of the Ace. If we were to play the game from here, the King would go to the bottom of the deck and we’d play the Ace face up. Since that’s the wrong order, we have to do some more management with our stack.
Start again. Pick up the Ace and put it face down in your hand. Put the King on top of the Ace. Now, take the card on the bottom of the stack and move it to the top. Next, take the highest face-up card and put it on top of the stack. Then, take the card on the bottom of the stack and move it to the top. Continue this pattern until all the cards are added to the stack, making sure that the last thing you do is move a card from the bottom to the top.
That stack is primed to go! Feel free to play the game out to double check, but you’ll see that the proper stack needs to be in the following order: 8, 2, King, 3, 9, 4, Queen, 5, 10, 6, Ace, 7, and Jack.
➡ Pro Perk: Chat With the Puzzle Coach!
Curious to know more about this particular problem and solution? Stumped by another riddle and want the secret to solving it? I’d love to hear from you. Email me with your questions and we can nerd out over all kinds of puzzles, math problems, and brain teasers together!
Richard Malena is a puzzle and game designer, creating codebreaking challenges for the launches of the Tomb Raider movie and Call of Duty: WWII, as well as for board games, film festivals, immersive theater, and all kinds of strange and esoteric endeavors. When he isn’t building puzzles, Rich is likely rewatching National Treasure 2: Book of Secrets and searching for hidden mysteries in the world.