# Questions tagged [cards]

For puzzles centered around playing cards.

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### Prove that we cannot arrange the cards according to the given rules [duplicate]

There are ten pairs of cards with the numbers 0, 0, 1, 1... 8, 8, 9, 9 written on them. Prove that they cannot be laid in a row so that there are exactly n cards between any two cards with equal ...
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799 views

### Card game with equal piles

You and your friend have come up with a new two-player card game. There are 15 distinct cards numbered 1 to 15. The first player orders the cards in some order of his choice and places them face down ...
• 25.1k
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### Are there truly unwinnable Calculation decks?

Calculation is a solitaire variant known for its large skill ceiling; supposedly, the large majority of games can be won by skilled human players, whereas the games to be won by uninformed play are in ...
• 1,758
490 views

### Transform a pile of cards in reverse order

There are 52 cards on a table and numbered in order from 1 to 52 with number 1 on top. The following operation can be repeatedly done: split the pile into two piles without shuffling and take cards ...
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709 views

### Number of cards to be pulled

Ten cards, numbered 1-10, are randomly dealt to 2 players, A and B, such that each player gets 5 cards. Before the cards are dealt, player A will say a number N. After the cards are dealt, A will ...
• 826
453 views

### Twisty puzzle composed of hexagonal prisms, with As and diamonds

(click to enlarge) My friend let me have a go of his cube and neither of us know what its called or where to buy one.
• 83
355 views

### The 7 face up/down card

Note: This puzzle is a very old puzzle I got from the Internet, however I changed it a bit to be more interesting. INSTRUCTIONS You have got 7 blank cards. You are playing with a friend of yours. Your ...
• 1,149
387 views

### Starred, as to the crew's aid

The flavour text (except for the puzzle's name) is not a hint, but a true story I didn't really have any ideas for a puzzle, but my everyday life gave me one. I think, the puzzle could be better if I ...
• 6,594
123 views

### Spider Solitaire - maximum number of cards in a single column

What is the maximum number of cards you can have in a single column of four-suit Spider Solitaire? The diagram below has 11 cards in column 2, more than any other column. Obviously, the correct answer ...
• 6,549
762 views

### What happened today? Asked the magician

Yesterday I went to a magic show and I was part of a clever trick. First of all, the magician arranged 36 cards in a 4 x 9 grid as follows: Then they called me on the stage. I felt a little bit ...
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205 views

### There are 49 cards here. Figure out what the seven facedown cards are and what position they're in

So here's the problem "There are 49 cards here. Can you figure out what the seven facedown cards are and what position they're in?" I have tried about everything in my math tool belt to try ...
1 vote
64 views

### Spider Solitaire - Minimum Guaranteed Turnovers

Consider the following game-state in Spider Solitaire. Although this game is not the most popular compared to others (e.g. poker, chess, backgammon etc) I assume the reader is familiar with the basic ...
• 6,549
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### Alice and Bob invent a game

The rain was still falling in Wales, and Alice and Bob were terribly bored of having to stay inside the caravan. With just a deck of cards to entertain them they had played all of the card games in ...
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531 views

### Captain Pun plays cards

Last night I was playing a game of cards with my good friend Captain Pun and his wife. All of a sudden, partway through a round, he threw down a card that bore this design: Colour-blind-friendly ...
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### Minigolf Solitaire

Golf is a form of patience (solitaire) in which you must remove cards from several tableaus, leaving as few as possible. Today, though, we're doing a round of Minigolf instead. Unlike Golf, there are ...
• 1,570
445 views

### Mathematical Coincidence

A friend came up to me today with a deck of cards, and put these 6 into a group: 2 3 5 7 J K The other 7 values went into another group: A 4 6 8 9 10 Q He then challenged me to find the reason ...
• 6,750
198 views

### What is the name for this meta magic-trick? [closed]

In his book Intuition Pumps and Other Tools for Thinking Daniel Dennett describes a system of layering magic tricks in the following way: There are some effects—they can hardly be called tricks—...
• 129
858 views

### Queens full of jacks

(Note: I doubt that this puzzle is complex enough to post it here, but I still took a try.) There are 3 queens and 2 jacks (a full-house combination from poker) taken from a deck with standard suits, ...
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### Alice and Bob play at cards

To pass the time Alice and Bob play a simple game of chance where cards are drawn in pairs from a shuffled standard 52-card deck. If two red cards are drawn Alice wins the round. If two black cards ...
• 386
149 views

### Approximate this big number using a binomial [closed]

Mr. Magico is a greater believer in this number: $$2^{50}=1,125,899,906,842,624‬$$ He also like to play cards, although he isn't fussy about the size of his deck, and nor does he care how many ...
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### Hiker’s Cabin Mystery | Pt. VII

Congratulations to @GarethMcCaughan for his victory on the long unsolved Part II of this mystery! Kudos! Part VIII will hold a not-so-fun twist! Solve this one quickly, and we can get to it! New ...
• 3,059
294 views

### What is the minimum High Card Points needed for a partnership to be able to claim all 13 tricks in Bridge?

Assume you have basic knowledge of how a contract bridge game plays. There are 40 total HCPs in a set of cards. 4 for each Ace, 3 for each King, 2 for each Queen and 1 for each Jack. What is the ...
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568 views

### Perfect riffle shuffles

Take a deck of cards (with indexed position from 1 (top) to 52 (bottom)) and perform a perfect riffle shuffle, such that the top card (1) is still on top and the bottom (52) is still on the bottom. ...
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222 views

### Randomly selecting cards using 6-sided dice

There is a pile of $5\leq N\leq15$ cards. $x=3$ or $6\leq N$ cards need to be randomly chosen from this pile (uniform distribution). To do this any number of $6$-sided dice can be rolled any number ...
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320 views

### A message sent to me in spell cards

My brother went missing a few days ago. No one has seen him since then. The day he went missing, I saw the following arrays of my new Dungeons and Dragons spell cards. I didn’t think much of it then, ...
• 9,688
143 views

### make a sum with cards

Take the numbered diamond cards in a standard deck, that is those from 2 to 10. You may use some of them to form a sum: for example 23+45=68. What is the maximum result you may obtain? I hoped there ...
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1 vote
1k views

### How many Dobble symbols are there? [closed]

The game of Dobble (will edit in a link later) involves a set of bespoke playing cards covered in symbols or small pictures - a dog, an arrow, a pencil, a tree etc. Each card contains eight such ...
• 2,106
711 views

### A cooperative guessing game - Guess your order and card

6 players sitting in a circle and each assigned a card among 2 Hearts, 3 Hearts, ..., Ace Hearts (i.e. any of the Hearts cards). Holding her card above his forehead (i.e. Indian Poker fashion), each ...
• 203
1 vote
127 views

### The magic trick [duplicate]

I am here to tell you about two brothers that were doing a magic trick. But not the kind with smoke and mirrors but just a deck of cards and the magic of the human mind. Will you be able to match the ...
• 391
137 views

### A complex problem from Garena 2017 challenge [duplicate]

The problem is quite complex and I would really like to know the solution.
2k views

### Pick one card magic

At a dinner last night, my friend Lan did a magic trick. Any ideas how it worked? First, Lan took a number of cards out of a 52-card deck. I don't know exactly the number of card. To be sure that the ...
• 181
236 views

### Who's the winner of this card game?

During a round of a card game big two, two players decide to show off their hands. The 1st player has ♥3 ♥4 ♥4 ♥6 ♥6 ♥8 ♥8 ♥K, and the 2nd player has ♠7 ♠9 ♠9. It's the 1st player's turn, and he can ...
• 161
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### 98 Cards: Optimal Strategy with Rule of Ten's

I recently found the game "98 Cards" by VdH and wondered if there is an optimal strategy to play it. Rules: There is only one player. Cards with each of the numbers $2$ to $99$ are ...
• 553
840 views

### Card trick with two assistants giving two cards each from a 53 card pack (with joker)

A long time ago, I saw on a website (with a grec sounding name i can't remember), a card trick I've passed a long time trying to solve. I hope it has never been posted there and i'm sure it will ...
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211 views

### How the best card can I choose?

Me and Varun playing a game of cards (standard deck of 52 cards). In which we distributed 5 cards to each other. Edit: We have seen each other's cards. We have to put the cards in a line one by one ...
• 378
273 views

### Named after - card puzzle

(this is a picture puzzle) Hint is -'Named after'
• 191
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### A retroanalysis problem in bridge

This is an entry into the 29th fortnightly topic challenge - Retrograde Analysis. You're passing a bridge table when one of the players (South) is called away suddenly. He gives you his hand and says ...
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### 6 Cards, Top to Bottom

The six cards shown below were turned face down, "shuffled" (i.e.. re-arranged), and put in a pile, one on top of each other. Each card has an obvious numeric value. In addition, the "J", "Q", and ...
• 569
3k views

### 5 people each have 5 equal cards

A competent logician is playing cards with four of his friends, so that there are a total of 5 people sat around the table. Each player has the same 5 cards, showing A, 2, 3, 4, and 5 (Ace being low). ...
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1k views

### Unique representation ID for 5-card poker hand using combination without sorting

There is a deck of 52 playing cards (e.g. poker cards). Assign every card a unique number (ID) at will. Every combination of 5 of these cards (a "hand") shall be represented by a unique result number, ...
590 views

### Dr. G's Interesting Theorem on Playing Cards

Dr. G has spent his last weekend with analyzing $n$ number of cards which are numbered from $1$ to $n$. He has a fair shuffling machine for his cards and while playing and drawing some cards, he uses ...
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351 views

### Optimal solution to a modified poker game

Note: Knowledge of the poker game Texas Hold-em is (probably) needed in order to answer this question. You and a friend (only two people are playing) are playing a standard game of Texas Hold-em but ...
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### Card Passing Game

13 friends are sitting around a table. They shuffle a half-deck of cards, consisting of only the black cards of a standard deck, and deal out two cards to each person. There are then a series of ...
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191 views

### Gambling with the gambler [closed]

You are walking on the street and notice a guy gambling with some other guys and you start to watch. The game principle is pretty easy. There is a standard 52-card deck and it is being shuffled every ...
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231 views

### 2 of 4 cards for 1 die

These are equivalent to using using a deck of 4 cards to emulate a 6-sided die. A. Assign integer values to   a, b, c, d   so that the 6 possible &...
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### In a Guess The Color game, what's the optimal strategy?

Here's a one-player card game: We begin with a shuffled card deck The player try to guess the color of the card at the top (black or red) If the player guess right, he can keep the card. Else the ...
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### Find the winning strategy for this card game

Nine cards numbered 1 through 9 are kept facing up on a table. Alice and Bob are playing a game wherein they pick up cards one at a time, alternatively. The first person to have three cards with sum ...
• 1,338
964 views

### Optimal game of Bluff (not the wikipedia one)

Rules Basics 52 well shuffled cards are dealt equally to both players. Player 1 starts the first hand. The game consists of a number of rounds, which are played as follows. On each round, players ...
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### Random Shuffled Deck of Cards

It is known that 7 random riffle shuffles are enough to make almost every configuration equally likely in a deck of 52 cards. Perfect Shuffle is when you cut the cards exactly in half and perfectly ...
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Both players are dealt $26$ cards from a regular $52$ card deck. He discards $1$ and makes $5$ hands (from the remaining $25$) in any order, each with $5$ cards. His score is given by the sum of ...