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# A Challenged Flight Deck

47 replies to this topic

### #1 plainglazed

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Posted 17 May 2012 - 10:06 PM

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?
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### #2 bushindo

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Posted 17 May 2012 - 10:13 PM

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?
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### #3 Morningstar

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Posted 17 May 2012 - 10:23 PM

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.

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The cake is a lie.

### #4 plainglazed

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Posted 17 May 2012 - 10:28 PM

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.
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### #5 Time Out

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Posted 17 May 2012 - 11:08 PM

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

Think this would work with mittens on too.
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### #6 plainglazed

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Posted 17 May 2012 - 11:41 PM

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!
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### #7 plasmid

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Posted 18 May 2012 - 12:35 AM

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.

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### #8 Morningstar

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Posted 18 May 2012 - 03:08 PM

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.
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The cake is a lie.

### #9 plainglazed

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Posted 18 May 2012 - 04:14 PM

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')
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### #10 plasmid

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Posted 19 May 2012 - 02:56 AM

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

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

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