47 replies to this topic

[plainglazed]

On the return journey from the Arctic Circle of Logicians Fresh Air/Fresh Ideas annual seminar, each pair of logicians received a complimentary pack of fifty two standard playing cards. These particular playing cards featured an image of the mighty de Havilland C-6 Twin Otter; the very aircraft they were currently shivering in. As such, each face down card would have one of two different orientations. The plane would either be pointing straight up against a sunless grey sky in an apparent death stall or, because of the slight tilt of its wings, would appear to be stuck in a sustained tailspin. Due to the logicians nervous desire for any distraction from the umhh, cold; they developed the following challenge: If a pair works together where only one knows the order of a shuffled deck and pre-arranges the direction of the plane on each card (without changing the order of the deck) and the other predicts the suit of each card, one at a time, from the evenly stacked face down deck, what scheme yields the maximum guaranteed correct number of suit predictions?

[bushindo]

On the return journey from the Arctic Circle of Logicians Fresh Air/Fresh Ideas annual seminar, each pair of logicians received a complimentary pack of fifty two standard playing cards. These particular playing cards featured an image of the mighty de Havilland C-6 Twin Otter; the very aircraft they were currently shivering in. As such, each face down card would have one of two different orientations. The plane would either be pointing straight up against a sunless grey sky in an apparent death stall or, because of the slight tilt of its wings, would appear to be stuck in a sustained tailspin. Due to the logicians nervous desire for any distraction from the umhh, cold; they developed the following challenge: If a pair works together where only one knows the order of a shuffled deck and pre-arranges the direction of the plane on each card (without changing the order of the deck) and the other predicts the suit of each card, one at a time, from the evenly stacked face down deck, what scheme yields the maximum guaranteed correct number of suit predictions?

I'd some some clarification. In the bold part, does it mean that the second logician predicts a card, the card is revealed, and then the logician makes the next guess, and so on?

[Morningstar]

Do the card designers have some personal vendetta against the manufacturers of the de Havilland C-6 Twin Otter? (I'm imagining cards all with different pictures of de Havilland planes suffering catastrophic structural failures).

Edited by Morningstar, 17 May 2012 - 10:23 PM.

[plainglazed]

I'd some some clarification. In the bold part, does it mean that the second logician predicts a card, the card is revealed, and then the logician makes the next guess, and so on?

that's correct. the first logician arranges the orientation of the cards without changing the order in some predetermined system then places the evenly stacked deck face down. the second logician predicts the suit of the top card, that card is revealed, then the back of the next card and its orientation is revealed, the suit of that card is guessed, etc.

had struggled with the wording. hope that helps?

Do the card designers have some personal vendetta against the manufacturers of the de Havilland C-6 Twin Otter? (I'm imagining cards all with different pictures of de Havilland planes suffering catastrophic structural failures).

nah, the same image is one each card. orienting the cards plane up or down just gives a "bit" of info to the other logician who does not know the order of the cards.

[Time Out]

Spoiler for <br />?Can the hand used to reveal the suite be changed<br />

Agree that a particular orientation means red suit and the other means black suit.
After a guess is made the hand used to turn the card indicates the suit of nex cardt, say
left hand is club/heart and right is diamond/spade.

Opening gambit could be signalled by an open palm gesture left/right as above.

Think this would work with mittens on too.

[plainglazed]

hmm, guess that again works making a max of 51? let's say the only info the second logician receives is the orientation of the top card of the remaining deck, the cards already revealed, and the orientation of all previous top cards.

EDIT: oops, had missed your play for determining the first card. also failed to mention my doubts as to the ability of even the wiliest of logicians to flip over a playing card from a stacked deck using either hand - wearing mittens!

[plasmid]

I can think of a strategy that will guarantee that at least half of the cards' suits will be correctly predicted fairly easily. I'll ponder a little further and see if I can do any better.

Edited by plasmid, 18 May 2012 - 12:36 AM.

[Morningstar]

nah, the same image is one each card. orienting the cards plane up or down just gives a "bit" of info to the other logician who does not know the order of the cards.

I know. I was being facetious. Sorry. Anyway, I have an idea, but it's not very efficient. I'm working on it.

[plainglazed]

I can think of a strategy that will guarantee that at least half of the cards' suits will be correctly predicted fairly easily. I'll ponder a little further and see if I can do any better.

yeah, think you can do at least a little better. good to know you're on the case.

I know. I was being facetious. Sorry. Anyway, I have an idea, but it's not very efficient. I'm working on it.

suspected as much but didn't want to just leave you hangin' (@ 15,000')

[plasmid]

A slight tweak of my initial approach would on average do a little better than getting half the suits right, but still can't guarantee more than half. For the sake of getting at least one strategy out to start things off...

Spoiler for

Set up the deck so that if a card is of one particular suit, say spades, it's oriented with the plane right-side-up. Any other suit and the plane is upside-down. The guesser will always guess spades if it's right-side-up and be guaranteed to get all of those, and will always guess one pre-determined other suit if it's upside-down, say hearts, and get all of those suit right as well.

On average you can do a little better by modifying the strategy: Keep a running tab of how many times each suit has already shown up - or more importantly, how many of each suit are still left in the deck - and use that to base the card orientation and guesses on. If the next card is of the most abundant suit left, then it gets oriented with a right-side-up plane and guessed correctly. Otherwise, it's oriented with an upside-down plane and the guesser guesses the second most abundant suit left. If there are multiple suits tied for most abundant, they would have to agree on a precedence of suits ahead of time to know which suit will be denoted by a right-side-up plane (say spades > hearts > diamonds > clubs) and the right-side-up suit would be whichever one is highest on the precedence list of those that are tied for most abundant.

The second strategy would lead to more cards being correctly predicted on average, but would not guarantee more than half.

Edited by plasmid, 19 May 2012 - 02:57 AM.