Can anyone explain how this is the correct answer?

Question

I'm bewildered as to how this should work.
Any ideas?

http://answers.yahoo.com/question/index;_ylt=AuaCbq4zcbPlyLoQAkipE6Xty6IX?qid=20070622063146AAMUWmP&show=7#profile-info-dc8j6AL0aa

Answer 1

That answer is incorrect. Okay, there are 20 coins, spread randomly amonst 80 other coins, making a total of 100. If I were to move 20 random coins and flip them over, I can have any number of heads-tails combination since I do not initally know which are heads and which are tails

Answer 2

If you don't understand the "20" method consider the following...you moved all 20 heads up to the other table, leaving 80 tails up. Now flip the 20 over...you have zero heads in both piles.

If in the 20 moved you have zero heads, the flip will generate 20 new heads...20 on that table and 20 on the table with 80 coins.

Any number of heads moved in between will generate the correct number.

#heads moved in 20 / #remaining in 80 pile / #heads after flip
0/20/20
1/19/19
2/18/18
...
20/0/0

Answer 3

1st of all, you can't guarantee that there will be an equal amt. of "heads up" coins, only within a certain %, say if it'sdone an infinite num of times.
Anyway, when you move any 20 from the 1st to the 2nd table, with each grab, there is a 20% chance that you'll grab a "heads up" coin, given those odds, out of the 20 coins on the 2nd table, 4 will be heads and 16 will be tails.
On the 1st table, 16 will be heads and 64 will be tails.

Flipping all the coins on the 2nd table turns the 16 "tails up" coins to heads up coins, therefore matching the 1st table.

Answer 4

It doesn't matter which twenty you take from the original 100 which has 20 heads up. Take away any 20 and reverse them and there will be the same number of heads up in both piles.

Take away 20 of which 5 are heads up. Leaves 15 heads up and 75 tails in the original stack. Flip the 20 and you have 15 heads up in the '20' stack.

Answer 5

Wow! that still makes no sense to me. How can you "assume" that you RANDOMLY picked out 15 tails and 5 heads WITHOUT LOOKING? Even if you take probability into account. There would be 20% heads, meaning of the 20 "randomly" selected coins only 4 would be heads. Either way, its only probability, like the other guy before me said, there could be any possible combinations of heads and tails. For examples, I could select all heads and turn them over to make all tails.

LOL. Ok I get it now thanks johnny. I am having an off day.

Answer 6

Just make sure the 20 heads up coins are in a group furthest away from you. When you grab coins, grab the ones closest to you (they will all be heads down). Turn 20 of them over. That puts 20 face up on each side.

Answer 7

It is easier to imagine with smaller numbers. Take ten coins, three are heads, now separate three and flip them. If you have separated all three heads, you flip them to tails and both piles have zero heads. If you have separated tails and flip them, now each has three heads. So, no matter whether you have pulled a heads or tails, flipping it equals it out. Try different combinations. Just remember, to separate the same number of coins as number of heads you are starting with.

Answer 8

It is easy actually....

You have 20 heads up coins in pile A

you take away 20 coins (some heads some tails)

Assume you took away 5 heads and 15 tails....
it will leave you 15 heads in pile A

Now flip pile B over and you will have 15 heads pile B


The number of heads will always match.

Answer 9

It isn't really. The answer should have been to move 10 coins to another table, heads up. then turn 10 of the heads up coins from the first table heads down. The guy who got best answer made the question look dumb.

Answer 10

i think he culdve just felt on the coins cuz that answer confused me too