Talk:Missing dollar riddle/Archive 1

Vote for Deletion
This article survived a Vote for Deletion. The discussion can be found here. -Splash 03:27, 31 July 2005 (UTC)

Explanation Confusing
So people get mixed up between the $3 the ladies got back and the $2 in the waiter's pocket. Happens all the time. Most people figure this kind of thing out and say "how could I have been so stupid." Seems like a rather involved explanation, which will only confuse people. I summed it up in one line at the end of the article.24.64.223.203 00:55, 14 October 2005 (UTC)

Clarity in its worst form...?
It is interesting how clarity has been proposed on this article, resulting in malformed english version of simple engineering questions. What makes this article work is not the myriad of solutions and explanations, but: a) how the misdirection works; b)what is the proper way to analyze circumstances where conservation is an issue, and; c) how the presentation deflects away from the proper analysis.

I am not perplexed that there are, and will always be, repeated attempts to offer english language solutions, as folks' internal analysis will be as varied as personalities. But I would like to suggest that the explanations offered digress from the real value of the article.

Before I change these new rounds of amendments to the article, perhaps some discussion is worthwhile... — Preceding unsigned comment added by JohnRuskin (talk • contribs) 16:07, 24 January 2007 (UTC)

(moved comment to bottom)
I think that it's too redundant, explaining the same things several times. I say go ahead if you think you can make it better; remember, be bold! | A ndonic O Talk · Sign Here 17:23, 24 January 2007 (UTC)

Clarity comes from solution paths without declarative points
It is interesting that the current verbiage for the 'solution' begins with and continues with declarative statements. It is these declaratives that could become a source for misdirection and confusion! I disagree that there is redundancy. The solution explanation and technique that disappeared relies on engineering and/or accounting principles; the "solution path", i.e., the proper solution path, is what should be emphasized by the article, not just the fact that any number of equations can be written which may or may not be wrong. — Preceding unsigned comment added by JohnRuskin (talk • contribs) 23:44, 15 March 2007 (UTC)

Article title
I'm concerned that the title to this page is wrong: it's not actually a paradox, and should not be defined as such. We all know a paradox when we see one: using one line of reasoning, a certain truth should hold, but the definition of the issue requires that that truth NOT hold, so we are left in a circle of reasoning. This isn't like that at all: it is simply an arithmetic error. —The preceding unsigned comment was added by Dac2chari (talk • contribs).


 * True, but it is usually called the missing dollar paradox, and we want to reflect the literature. It isn't our business to correct illogical terminology others use. --Sopoforic 08:46, 21 April 2007 (UTC)

Untitled 1
Please fix link. — Preceding unsigned comment added by 146.18.173.72 (talk) 19:27, 19 May 2007 (UTC)

An attempt to retrain intuition
Replace 30 with 3000, 10 with 1000, 25 with 2500, therefore 5 with 500, BUT 2 with 497, and therefore 9 with 999 and 27 with 2997, also noting that 3 is thus not replaced. Now you wouldn't add 2997+497 to account for the monies, and then wonder about the "extra" 494 (=3000-2997+497), would you? Does this help? — Preceding unsigned comment added by ChangChienFu (talk • contribs) 15:27, 23 July 2007 (UTC)

Alternate Solution
The alternate solution suggested in this article is mathematically incorrect and without being labelled as so will only confuse others who read it. —Preceding unsigned comment added by 203.166.109.197 (talk) 15:08, 24 October 2008 (UTC)


 * The alternate "solution" referred to above, which I have now deleted, went as follows:


 * 1) Divide $25 between the three men to get the true amount each paid for the room.  25/3 = 8.333
 * 2) Add the extra dollar that was given to each man by the bell boy.      8.33+1= 9.333
 * 3) Multiply each of the three men's contributions, we get the total amount paid.  9.333 x 3 = $28
 * 4) Add the two dollars kept by the bellboy. $28 + 2 = $30


 * I have no idea whether this was someone's actual conceptual error or a witty joke -- it accepts the false suggestion of the original "paradox" (the idea that the bellboy's cut and the amount paid by the guests should add up to $30) and makes it appear that, by gum, they do add up to $30, because the guests paid an additional dollar that got lost in fractions somehow. But as in the original puzzle, we are doing operations we have no reason to do:


 * "Divide $25 between the three men to get the true amount each paid for the room." But they never paid $25 for the room. They paid $30 initially, or $27 net, after their $3 refund is applied. $25 is a logically different entity, the amount kept by the clerk.


 * The completely unnecessary dividing by three in line 2 and multiplying by three in line 3 is a bit of misdirection to make us think that somehow the "missing dollar" got hidden in fractions. If you simplify these unnecessary operations out and relabel the quantities correctly, you get:


 * 1)  Amount guests should have paid, the amount kept by the clerk, is $25.
 * 2)  Add the $3 given back to the guests. (But remember it is only part of their overpayment.)
 * 3)  $25 plus $3 equals $28. (Mathematically true; but it does not represent the "total amount paid," as the Alternative Solver claims.)
 * 4)  Plus the $2 of the overpayment kept by the bellhop equals $30 (the actual total amount initially paid.)


 * Now, why are we trying to add up to $30, unless we are looking for the original total amount paid? How could the "total amount paid" plus two dollars equal the total amount paid? This is a worse example of mislabeling terms than the original "paradox," but I don't think it's an honest mistake. In any event, it does not belong here as an "Alternate Solution," as it neither resolves nor clarifies the original puzzle. 209.181.57.144 (talk) 05:48, 3 February 2009 (UTC)

Reworked Solution
I tried to simplify the solution a bit. The previous one made sense only after I spent the time to derive it again. I may have fallen into the same trap though, so feel free to clarify further if it is still confusing. MichaelShoemaker (talk) 21:57, 2 February 2009 (UTC)


 * Rightly or wrongly, I think I have provided the much simpler and clearer solution we've been going for, cutting out some true but overcomplicated ways of looking at it (and deleting the false "Alternate Solution" for reasons explained below.) Strictly speaking, the cash flow analysis at the end is no longer necessary, either -- not to explain the puzzle. But I let it stand as an example of a tool for analyzing this sort of problem in general. 209.181.57.144 (talk) 06:29, 3 February 2009 (UTC)

Needs to be rewritten maybe here?
The explanation is still not clear. Could someone maybe put a walkthrough on the discussion page for those who can't understand the brief explanation? After reading the discussion, I'm glad I'm not the only one who still doesn't understand the explanation as it is written on the main article. Sentriclecub (talk) 02:11, 30 March 2008 (UTC)

Personally, I think the solution is actually brief and I do not understand the lengthy explanations that are currently in the article. It seems like an almost desperate attempt to sound smarter.

To that end, I have shortened the Solution portion of the article. Hopefully it's a tad clearer. It is certainly shorter. We'll see how that pans out. We might want to reconsider the various explanations that have been given. They add length to the article, and may be of interest to some, but are probably unnecessary clutter that could be deleted and replaced with external links where applicable. —Preceding unsigned comment added by 74.79.229.63 (talk) 22:10, 12 November 2008 (UTC)

Additional question: I still don't see how the math doesn't work. I understand the process of coming up with the 30 on the main article, but why doesn't the (9*3)+2=30? Doesn't it make perfect sense that the three people paid 10$, and each of the three guests were given a dollar back--so each paid 9$? The bellboy kept 2 dollars, so why doesn't it add up to 30$?

Let me work backwards: 30 for meal. 5$ handed back. Bellboy had 2, and guests (in total) have 3. Each guest really paid (10-the one each received back=9) Three guests paying 9 each plus the bellboy's 2 still comes to 29. I'm messing up somewhere; may I ask for assistance? Who can help me?


 * Guests originally pay $30 and bellhop only gives them a $3 refund, so they have paid $27 and (here's the important part) that unrefunded $27 includes the bellhop's $2. To get back the original $30 you have to add the $27 unrefunded and the $3 refunded. Adds up, right? But the puzzle asks you to add the $2 already included but forget the $3. Consequently, you wind up a buck off. See if the new wording of the solution makes this clearer. 209.181.57.144 (talk) 07:48, 3 February 2009 (UTC)

In a nutshell, the problem is is that you're trying to add the amount that the men paid(it is not with them) with the amount that the maid or whatever kept to herself(it is with her). This results in adding the 2 dollars to the 27 dollars it is already included in. Remember that the guests are essentially paying for the rooms and the 'tip' kept by the maid. The amounts are manipulated so it looks like one dollar was lost somewhere, but it can be done with any amount. The guests payed 27 dollars, 25 went to the hotel, 2 to the maid. The missing three are with them. —Preceding unsigned comment added by 195.222.43.25 (talk) 09:47, 30 April 2009 (UTC)

Tried to clean it up
As stated earlier, the explanation is vague and the writing's tone and style don't help clarify the article. I tried to clean it up, mainly focusing on the specificity of the summary at the top of the page. I didn't do a very good job, though. Let's clarify the thesis of the article, the summary, and that will direct the organization. What is the importance of this riddle? I think that there's a hearty and enlightening idea in this article, but I just can't seem to state it clearly and succinctly. Vrtt (talk) 08:48, 7 July 2009 (UTC)