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37 votes
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A five card trick - How does it work?

I'm going to assume Alice looked at the cards and chose which one to give back to you. The key to the puzzle is then to encode a single card's suit and value in 4 cards without the luxury of choosing ...
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29 votes
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Alice and Bob invent a game

So building on kristinalustig's answer they are indeed playing The cards are assigned as follows Alice's first turn Bob's first turn In particular Alice's next move produces Bob's next move ...
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25 votes
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Poker and a card shark

It changes...
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23 votes
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Minigolf Solitaire

Whilst I tried to split things logically into blocks (e.g. working forwards to a point, then working backwards from the end to see what else was left, and thus needed to be used first), this was ...
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21 votes
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How to cheat at cards

The probability is If you
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20 votes
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Find the winning strategy for this card game

This game is actually... Therefore,
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17 votes
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Multilayer Image Steganography

The final answer is: The clue "listen" pertains to audio files embedded in the images. The legend for the blue layer is four cards. The file is an OGG Opus file. The audio is someone saying "If ...
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17 votes
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Unique representation ID for 5-card poker hand using combination without sorting

If we take the IDs to be and the result to be then you can find the card IDs by and the number will be at most We can actually do better than this while using the same basic idea: A little better:...
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17 votes
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Pick one card magic

If cards are not prearranged then it is impossible to do this trick. It is so simple arrangement that you wouldn't notice. Because Lan got your card by This way
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17 votes
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Perfect riffle shuffles

Bonus:
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17 votes
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Captain Pun plays cards

I believe the message being communicated is Getting the message took a bit of guesswork, but it checks out: Since
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16 votes

A five card trick - How does it work?

Here is my answer: Key Item 1: Key Item 2: Key Item 3: Key Item 4: Key Item 5:
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16 votes

Alice and Bob invent a game

I spent quite a while working on this yesterday and today. I only have a partial answer. I started with the assumption that I chose this assumption because: Given this assumption, I tried: However:...
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13 votes
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The Fitch Cheney Card Trick Extended

Strategy without the Joker Say you take any five cards from a deck. Since there are only 4 suits, there must be at least two of them which have the same suit. One of these will be our chosen card ...
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13 votes
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Transform a pile of cards in reverse order

The optimal strategy takes Here's why this is necessary: And here's a way to do it: Fun fact:
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13 votes
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Card game with equal piles

Base question Addition: Bonus question
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12 votes

A five card trick - How does it work?

This is a great card trick known as Fitch Cheney's Five Card trick. Alice selects the fifth card to be identified and arranges the remaining four cards in a specific sequence. Then Bob interprets the ...
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12 votes

Rigged casino that prevents pairs

Here is a permutation that works upto n=12: ...
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  • 2,438
12 votes
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Two Card Probability Problem

Use a random source to pick a number from 2 to 13. If it is equal or less than the value of the card you picked, keep the card. If it is greater, switch. Thus, if you turned over a 1, you always ...
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12 votes
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5 people each have 5 equal cards

Assuming each player wants to maximize their personal win probability for the single game... The reason I chose this approach is
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11 votes
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The Great Houdini's awesome card guessing trick (3)

Answer: The strategy:
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  • 3,817
11 votes

5 people each have 5 equal cards

Assuming he respects his friends, he assumes they play just as he will. In order for him to have the highest chance of victory, he needs to be able to select each card with a random probability. The ...
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  • 8,992
11 votes
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A retroanalysis problem in bridge

6 rounds have been played and no-one has any voids before you sit down. There are therefore at most 1 round of spades and hearts (if there were 2 then 8 cards are played + 4 visible + 2 with the ...
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11 votes
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Twisty puzzle composed of hexagonal prisms, with As and diamonds

It was first released in June 2004 by Mefferts under the name Jackpot, and later it was renamed Platypus, and after that the New Generation Puzzle. It probably was sold under other names as well. See ...
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10 votes
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The Great Houdini's awesome card guessing trick (1)

The smallest possible of correct guesses is max(a, b, c, d): every other suit could come up first and he would guess the most likely one over and over until nothing ...
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10 votes
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The Great Houdini's awesome card guessing trick (2)

Here's a proof that 26 right answers is optimal for the worst case. Without loss of generality for the worst case, Houdini's strategy is deterministic, and the adversary knows it and can pick cards ...
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10 votes
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How To Split The Deck

The criterion was: Note:
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  • 2,609
10 votes
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Random Shuffled Deck of Cards

No amount of in-shuffles and out-shuffles will approach a random shuffle. Let's say that two cards mirror each other if they are the same distance from the middle of the deck. This means that the $i$...
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10 votes
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Card Passing Game

Let us begin with this observation: with 13 pair of cards in play, that accounts for every card in the half-deck. There are no cards remaining out of play. So let's construct a scenario in which ...
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10 votes
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Mathematical Coincidence

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