Maths Puzzle: Coins Solution

Take a random pile of coins. If I tell you how many coins are heads and how many coins are tails, can you separate the pile into two piles with the same number of heads in each. And can you do this with your eyes shut?

Take the same number of coins as there are heads. Call this pile 1. Then;

Total number of coins in pile 1 = Total number of heads

In other words, if h1 and t1 are the number of heads and tails in pile 1, and h2 is the number of heads in pile 2, then;

h1 + t1 = h1 + h2

Cancel h1 on both sides and you will see that the number of tails in pile 1 will be the same as the number of heads in pile 2. So, if you turn over all coins in pile 1 you will now have the same number of heads in each pile.

[singingbanana]

@TyYann Thanks Yann, tried to explain it without the equations. If people liked this you should check out Yann's channel for more of this sort of thing.

[singingbanana]

@thomaste33 The puzzle is, if you are told how many heads there are can you separate them into two piles with the same number of heads in each pile, with your eyes shut.

[TimelordUK]

I just adore your energy and enthusiasm! Happy Christmas to you x

[LittlePeng]

Yes it will. You now you have 7 heads. So you take all 7 coins to second pile and flip them. Then you have 0 heads in second pile, and 0 heads in first (empty) pile. Mathematically, this is correct, but one of piles is empty. But if you have 7 coins, and you know that 7 of them are heads, challenge is trivial

[singingbanana]

@PurpleUkuleleGuy That line was entirely for Brian :)

[hhnfaa]

If you took two black coins, that means there were two white coins in the original pile, so you'd have two in each pile. Still works. It works for any number of coins, every time.

[Error]

Well said, Doc Jim. I talked to a legendary maths professor at my university today for the first time, and I posed the Salem Witch Trials puzzle to him. He figured it out fairly quickly, but he really liked it :).

Also, I've gotten 6 new subscribers just from the shout out in the description :D.

[GetMeThere]

I'm totally fascinated by this problem! Thanks for posting it.

[singingbanana]

@watrick144 Yup, there's nothing special about heads.

[JustLilGecko]

I feel smarter every time I watch a singingbanana video.

[singingbanana]

@Error081688 I love the Salem Witches puzzle. People may like to dig further back into my videos to find it, it was a puzzle me and my friend Colin made up. And I hope this bump in the comments helps you get more subscribers, it was Tom here that gave me the puzzle, and I love it.

[singingbanana]

@ffcloud19 Maths isn't just equations, but about logic and problem solving. So this is maths. But this can be described with a couple of equations, and I've put them in the description.

[Weirdgus]

the probability of that is 1 in 2 at the power of 7 so on average in one out of every 128 attempts you should flip all heads(or all tails for that matter). That's why you should do it with 10 or more coins. (he does exemplify it with 11 in the video, in that case the probability of flipping all heads would be almost 16 times smaller than in your case since 2^11 = 2028

[anticorncob]

@miketheman1393 Here's one that's even harder.
Suppose a robot is walking. When x seconds go by, he is walking x miles per hour.
Another robot is a mile away facing the first robot. When x seconds go by, it is walking 2x miles per hour.
When will the robots meet?

[Cosmicextry]

@singingbanana Maybe watrick144 was asking if you could still get the same number of heads in each pile (as initially requested) when given the number tails from some random pile. [For example, you see that your black faced coins did not match up (except for the trivial example).] If you don't know the size of the pile, this does make it a slightly different problem. However, it would still be solvable with the same algorithm used in this video (after a simple added step at the beginning).

[LeftRage]

1. Remember which ones are black.
2. Close eyes.
3. Flip all of the coins you remembered to the other side.
4. Feel how many coins are on the table (should be an even number).
5. If you have 10, put 5 pieces on each side. (8-4, 4-2, 2-1, you're not stupid).
6. Open eyes.

Ta-da!

[claudioestevez]

Funny how he just casually throws in that you can also use this for a scam

[cardiganmimi]

@Montero201414 Yes, trivially. Take 11 coins and flip 'em all over. Then one set has 0 coins, while the other has 11 coins, neither of which have any heads. @Horinius what in the world are you talking about??

[singingbanana]

@2ndAge Haha! Brilliant. But I will be taking 30% of all future earnings.

[jeremiahmacdonald]

You know how people get songs stuck in their heads? Well I've got his "Hello Everyone!" stuck in my head!