The Missing Dollar

I posted this in Chit Chat, but I think minds such as the ones here can tell me:

Quote:

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Two friends go to a small shop. They decide to purchase a small radio/cassette player for $50. They each pay $25 and take it away.

The shopkeeper suddenly remembers that the cost of the radio was actually $45, so he sends his assistant along with $5 to give back to them. The assistant thinks to himself, "What the hey, I'll keep $2 with me." The assistant catches up to the two friends and gives them $3, and goes back.

Now, each friend had paid $25, and they got $1.5 back, each.

25-1.5 = 23.5. So, they each paid $23.5 for the radio.

Combined, they paid...$23.5 + $23.5 = $47 for the radio.

There's $2 in the assistant's pocket.

$47 + $2 = $49.

Wait a minute, they paid $50....
Where is the missing dollar?

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??

Edit: Serious answers please.

Your problem is very similar to this one:
http://161.58.186.97/showthread.php?...missing+dollar

I haven't got time to read them through in depth because I've got to go to college. I'll check them later.

True. I know that it can be solved using a state diagram. There is no missing dollar. But I wanted to know that even though the method used here is correct, it yields an incorrect answer. If you approach it backwards, there is no missing dollar. But when you approach it this way, which is legitimate, there's some sort of an error.

I wanted to know why this error occurs, sorry I didn't mention it in the first post. There's no point following the chit chat one, cz everything there just turns into a joke.

Any explanations? Is it a flaw in mathematics or am I just paranoid or am I stoned? (Green day :D)

Well to be honest it's all a bit beyond me ;) . Ask Guv, keda or NotLKH and they'll probably help you out.

I've just finished a 2hour tuition session with my maths tutor on if and only if, iff, implication etc etc (repeat to fade). My head hurts.

The trick, here, is to be careful where you subtract from.

The two friends pay $50, so $50 goes to the owner. The owner realizes the radio cost $45, so he takes $5 out, therefore, he's left with $45.

Here's another way to think of it. Each person paid $25, but they got $3 back, so they each paid $23.5. That gets us a total of $47. But since the assistant kept $2, we are left with $45.

Megatron, you're making some sense. Now I'm a bit confused. I'll go over that carefully and see if my head doesn't explode.

Quote:

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Originally posted by mendhak
Megatron, you're making some sense. Now I'm a bit confused. I'll go over that carefully and see if my head doesn't explode.

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how's your head?

Ya, this was fun to think about...

the problem is when you go from each paying 23.50 which is
$47 in total you try and get back to $50, but that aint the case anymore,
now you need to figure out why they OVERpaid cause the radio was only $45.

see?

And that "overpay" was the $2 that the assistant kept in his pocket.

Quote:

---

Two friends go to a small shop. They decide to purchase a small radio/cassette player for $50. They each pay $25 and take it away.

The shopkeeper suddenly remembers that the cost of the radio was actually $45, so he sends his assistant along with $5 to give back to them. The assistant thinks to himself, "What the hey, I'll keep $2 with me." The assistant catches up to the two friends and gives them $3, and goes back.

Now, each friend had paid $25, and they got $1.5 back, each.

25-1.5 = 23.5. So, they each paid $23.5 for the radio.
Combined, they paid...$23.5 + $23.5 = $47 for the radio.

There's $2 in the assistant's pocket.

$47 + $2 = $49.

Wait a minute, they paid $50....
Where is the missing dollar?

---

this is easier on the brain if it's one person

45+3 = 48 assisstant gives 3 back (45 + 3)
u were subtracting from the wrong cost.. that's wrong

There's $2 in the assistant's pocket.

$45 +3$ + $2 = $50.
this is how it should be: cost + money in their pocket + assisstant
not fake cost - money in thier pocket + assisstant money

oh and btw, 47$ (what they paid) + assisstant money + MONEY IN THEIR POCKET (3$) is 52, this is another reasont eh problem is so damn hard, the trick has been tricked...)

I like to see it this way:

There was £50 at the beginning.

The shop keeper has £45
The Friends have £3 between them (£1.5 each) £3
The messenger has £2
-------
£50
-------

Ta Da!

I found the real problem!!

Quote:

---

Two friends go to a small shop. They decide to purchase a small radio/cassette player for $50. They each pay $25 and take it away.

The shopkeeper suddenly remembers that the cost of the radio was actually $45, so he sends his assistant along with $5 to give back to them. The assistant thinks to himself, "What the hey, I'll keep $2 with me." The assistant catches up to the two friends and gives them $3, and goes back.

Now, each friend had paid $25, and they got $1.5 back, each.

25-1.5 = 23.5. So, they each paid $23.5 for the radio.

Combined, they paid...$23.5 + $23.5 = $47 for the radio.

There's $2 in the assistant's pocket.

$47 + $2 = $49.

Wait a minute, they paid $50....
Where is the missing dollar?

---

the 2$ in the assisstant's pocket is already counted in the 23.5$
It should be

There's 3$ in the friend's pockets.

Once again, I'll iterate that although these methods, like pointed out in the above few posts, may work, the weird part is that the calculations don't work the way it's been presented in the first post.

Then Megatron pointed out something, and I understood it for a while. And then a couple more ppl posted, which served to confuse everyone else. :D :p

heheh... I certainly hope it's not a flaw in mathematics...