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   the Infinite Quarter Sequence question

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Topic: the Infinite Quarter Sequence question (Read 22697 times)

dtang4
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the Infinite Quarter Sequence question
« on: Oct 13^th, 2003, 2:02pm »

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Hey, what's up?

This is my first post, and it's a plea... heh. Can someone give me some insight to this problem, found on the hard riddles section of the site:

You are wearing a blindfold and thick gloves. An infinite number of quarters are laid out before you on a table of infinite area. Someone tells you that 20 of these quarters are tails and the rest are heads. He says that if you can split the quarters into 2 piles where the number of tails quarters is the same in both piles, then you win all of the quarters. You are allowed to move the quarters and to flip them over, but you can never tell what state a quarter is currently in (the blindfold prevents you from seeing, and the gloves prevent you from feeling which side is heads or tails). How do you partition the quarters so that you can win them all?

I've been pondering this for at least the past 15 minutes and no worthwhile ideas yet. Thanks in advance.

PS. Has anyone heard the smurfs question, where they wear either red/blue hats and must guess which one?

dave

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towr
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Re: the Infinite Quarter Sequence question
« Reply #1 on: Oct 13^th, 2003, 2:34pm »

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on Oct 13^th, 2003, 2:02pm, dtang4 wrote:

This is my first post, and it's a plea... heh. Can someone give me some insight to this problem, found on the hard riddles section of the site:

It's allready somewhere in the forum, which has a search function you can use.
Basicly, you divide the quarters in two piles, one of 20 and one of the rest, then flip over the 20 quarters in the first.

« Last Edit: Oct 13^th, 2003, 2:35pm by towr »

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Wikipedia, Google, Mathworld, Integer sequence DB

BNC
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Re: the Infinite Quarter Sequence question
« Reply #2 on: Oct 13^th, 2003, 2:43pm »

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on Oct 13^th, 2003, 2:02pm, dtang4 wrote:

Hey, what's up?

This is my first post,

Welcome!

Quote:

I've been pondering this for at least the past 15 minutes and no worthwhile ideas yet. Thanks in advance.

15 min is not much. Most "hard" problem take longer.

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PS. Has anyone heard the smurfs question, where they wear either red/blue hats and must guess which one?

Sounds similar to this riddle

« Last Edit: Oct 13^th, 2003, 2:46pm by BNC »

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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]

dtang4
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Re: the Infinite Quarter Sequence question
« Reply #3 on: Oct 13^th, 2003, 3:28pm »

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re:towr
Great! thanks for the lead.

re:BNC
Thanks. Yea, but 15 minutes and no ideas on how to attack it.. heh.

Hmm, my puzzle is a bit different. I roughly skimmed the hard riddle (since I thought it was hard, heh) section and didn't find it. Here's the basic gist:

Gargamole (spelling?) captures a large group of smurfs and lines them up single file. He then places a hat on each one, either coloured blue or red. Each smurf can see all smurfs' hats before it but cannot see its own or any behind it. Starting from the back of the line, Gargamole will ask each smurf what colour hat it's wearing. If the smurf answers incorrectly, it will be eaten; else, it can leave free. He proceeds down the line till every smurf has either been freed or eaten. All the smurfs can hear preceding answers. They are not allowed any cheap play, like tapping their feet and stuff like that.

Before the fun begins, he allows the smurf to strategize a method of approach to save as many as possible. What should they do?

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