## Partitioning Quarters

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### Partitioning Quarters

You are sitting in front of a table, blindfolded and with heavy gloves on. On the table are 100 quarters, 20 of which are tails up. You can move around and flip the quarters but you cannot feel which side is which.

Your task? Separate the quarters into two groups so that the number of tails in both groups is equal. You are allowed to end with a different number of tails than you started with, as long as it's equal between the two groups you've made. Show a method that will work 100% of the time.

(You'll hit yourself once you get it.)

Patashu

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Did you check if hasn't been done before, in terms of some magic trick?
"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

3.14159265...
Irrational (?)

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Joined: Thu Jan 18, 2007 12:05 am UTC

Separate 20 coins from the other 80 and flip all the coins in the 20 group.
If there were X tails in the 20 group, then there are 20-X tails in the 80 group. After flipping all 20 coins, there will then be 20-X tails in the 20 group as well.

parallax

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### Wording?

Separate them 50/50. -You didn't specify tails up or down.
I don't know how 5E D&D will be played, but 6E D&D will be played with paper and pencils.
Wayfarers Role-playing Game. -Ye Olde Gaming Companye.

markkat

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Location: Mitten

Oops, is there supposed to be a solution thread?
I don't know how 5E D&D will be played, but 6E D&D will be played with paper and pencils.
Wayfarers Role-playing Game. -Ye Olde Gaming Companye.

markkat

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Joined: Wed May 02, 2007 4:37 pm UTC
Location: Mitten

I don't think it's necessary to conceal joke answers.

Cosmologicon

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Cosmologicon wrote:I don't think it's necessary to conceal joke answers.
I don't know how 5E D&D will be played, but 6E D&D will be played with paper and pencils.
Wayfarers Role-playing Game. -Ye Olde Gaming Companye.

markkat

Posts: 108
Joined: Wed May 02, 2007 4:37 pm UTC
Location: Mitten

So we're talking uniformly distributed, like
Code: Select all
`HHHHHHTHHHHHTTHHHHHTHHHHHHHHTTTHHHHTTHHHHHHHHHHHHHHHHHTTTTHHTHTHHHHHHHHHTTTHHHHHTHHHHHHHHT`
?

And putting them on their sides does not count?
The harder you try, the dumber you look

Spaz Funbag

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Throw the table through the window.
"GRRRRRRRRRROOOOOOOOWR!!!!"
(Translation: "Objection!")

Maseiken had the ball at the top of the key...

Maseiken
The Candylawyer

Posts: 2827
Joined: Sat May 19, 2007 11:13 am UTC

I change them for a 20- and a 5\$ bill, making those my two groups. Neither one has tails up, so i take the cash and spend it on ice cream.
The harder you try, the dumber you look

Spaz Funbag

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Location: Ja-Ma-Nee

Remove the blindfold with your heavily gloved hands, or what parallax said.

pete

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Maseiken wrote:Throw the table through the window.

In a blindfold? What if it hits the wall?

bbctol
Super Deluxe Forum Title of DESTINYâ„¢

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I was referring to the window that is created by throwing the table.[/i]
"GRRRRRRRRRROOOOOOOOWR!!!!"
(Translation: "Objection!")

Maseiken had the ball at the top of the key...

Maseiken
The Candylawyer

Posts: 2827
Joined: Sat May 19, 2007 11:13 am UTC

parallax wrote:
Separate 20 coins from the other 80 and flip all the coins in the 20 group.
If there were X tails in the 20 group, then there are 20-X tails in the 80 group. After flipping all 20 coins, there will then be 20-X tails in the 20 group as well.

you dont know what the other eitghty is.. so how can u do this???

i think we shoulddd throw this out the newly made window...
history repeats, we are the pattern
REMEMBER WILLIAM JAMES SIDIS

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Joined: Sat Jun 16, 2007 4:29 am UTC

You don't have to know. You just separate them into two groups, one 20 and one 80. The original problem said the groups didn't have to be the same size.

If the 20 coins you randomly selected included 5 tails, then that means there's 5 tails in the 20 group and 15 tails in the 80 group. If you flip every coin in the 20-coin group, this makes 15 tails. This always works, no matter how many coins with tails are in the randomly-selected group of twenty coins.

semicolon

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