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32 votes
Accepted

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 ...
hexomino's user avatar
  • 136k
23 votes
Accepted

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 ...
Alconja's user avatar
  • 37.3k
19 votes
Accepted

Captain Pun plays cards

I believe the message being communicated is Getting the message took a bit of guesswork, but it checks out: Since
phenomist's user avatar
  • 13.6k
18 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
prit.patel's user avatar
17 votes
Accepted

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:...
Gareth McCaughan's user avatar
17 votes
Accepted

Perfect riffle shuffles

Bonus:
noedne's user avatar
  • 15.4k
17 votes
Accepted

How many different kinds of hands can appear in a single Texas Hold 'em game?

I believe the maximum number of different hands is 7 Here is one such example:
Sconibulus's user avatar
  • 19.7k
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:...
kristinalustig's user avatar
  • 3,402
15 votes
Accepted

Card trick: guessing the suit if you see the remaining three cards (important is that you can't move or turn the cards)

Step 1: Step 2: Step 3: Step 4: Example:
ApexPolenta's user avatar
  • 2,834
13 votes
Accepted

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:
Deusovi's user avatar
  • 147k
13 votes
Accepted

Card game with equal piles

Base question Addition: Bonus question
Retudin's user avatar
  • 9,178
12 votes
Accepted

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 ...
Dr Xorile's user avatar
  • 23.6k
12 votes
Accepted

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
Sconibulus's user avatar
  • 19.7k
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 ...
kaine's user avatar
  • 9,112
11 votes
Accepted

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 ...
Jaap Scherphuis's user avatar
11 votes
Accepted

Mind Reading in Three-Handed Pot Limit Omaha

Suppose the board is: with Charlie (last to speak) holding To see how Charlie could infer the contents of Alice and Bob's hands, consider that... As a consequence, Alice's winning hand must be Bob,...
supercat's user avatar
  • 2,235
10 votes
Accepted

Mathematical Coincidence

Kalyan Datta's user avatar
10 votes
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What happened today? Asked the magician

The magician and the assistant need not memorize 36 phrases, because they have memorized the following simple table: Note that every sentence contains two nouns (or nominal phrases), and a verb. To ...
Ankoganit's user avatar
  • 18.7k
10 votes
Accepted

Pick cards from a table

I can get My thought process is I believe this is the maximum because I've made two pictures to help illustrate what's happening.
SQLnoob's user avatar
  • 8,570
8 votes

Pick one card magic

She knows your card because The key moment is at
Saeïdryl's user avatar
  • 3,040
8 votes

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

7S can be forcibly won with five HCP: ...
supercat's user avatar
  • 2,235
8 votes
Accepted

Number of cards to be pulled

Here's my solution based on expectations. First, The calculation steps are shown below: Next, let's think about A's strategy. Then, In conclusion:
Jerry Dean's user avatar
  • 1,746
7 votes
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6 Cards, Top to Bottom

Order (Am adding explanation) Step 1 See clue #3 Step 2 See clue #4 Step 3 See clue #2 See clue #6 Step 4 See clue #1 merging steps 3 and 4 since the last card is the king, we get the ...
Karan Atree's user avatar
  • 2,148
7 votes

A cooperative guessing game - Guess your order and card

As a starter, there is a strategy to make specifically to guess correctly. The strategy is By doing that, Take a note that The next step is by calling Hence, For bonus question, the above ...
athin's user avatar
  • 34.2k
7 votes

A cooperative guessing game - Guess your order and card

- So, the answer is six? - said A. - What are we aiming for now? It's no use trying to increase the six, since, ha-ha, there are only six of us here. And if there were more of us, I suppose, we could ...
Thomas Blue's user avatar
  • 6,952
7 votes
Accepted

A cooperative guessing game - Guess your order and card

Let's do better. I claim that we can fully win when: This can be done as follows: This seems to be tight:
phenomist's user avatar
  • 13.6k
7 votes

Minigolf Solitaire

I found a different answer by writing a python program to brute force find the solution using a depth first search(go as deep as possible until you can't make any more moves and then backtrack). I ...
Cruncher's user avatar
  • 719
7 votes

Mind Reading in Three-Handed Pot Limit Omaha

Supercat's answer is correct. Below is a more rigorous proof of its correctness. An example board is: On this board, the best possible 2-card holdings, in sorted order, are: In order for Alice to ...
dshin's user avatar
  • 1,533
6 votes
Accepted

Named after - card puzzle

  The person being named is...   ...as the missing cards’...   ...which are named for the person being named.   Without knowing about this person’s name, you ...
humn's user avatar
  • 21.9k
6 votes

5 people each have 5 equal cards

Looking at this from a statistical standpoint we know that we should never play a card higher than a 3. In all cases an A, 2 or <...
Scott's user avatar
  • 460

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