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Three friends brought 3 pens together each 10 dollars. Next day they got 5 dollars cash back so they shared each 1 dollar and donated 2 dollars. Now the pen cost for each guy will be 9 dollars (\$10 -\$1).

But if you add all 9+9+9 = 27 dollars and donated amount is 2 dollars so total 29 dollars.

Where is the other \$1?

Martin Thoma
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Jag
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  • Can it really be that we have nothing do close this as an exact duplicate of? Closing as "off topic" seems definitely wrong to me; the question of which calculations are the right ones to perform in a given (imagined) real-world situation shouldn't be off topic. We can call it a question about mathematical modeling if we want to be highbrow about it. – hmakholm left over Monica Aug 30 '13 at 21:46
  • I upvoted the question to make up for a downvote. Questions far stupider are asked here all the time and many receive lengthy answers. – Stefan Smith Aug 30 '13 at 22:53
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    @Henning, it's actually a nice example of a fallacy in mathematics (like the 1=2 equation where one divides by zero). Do you agree in creating a "fallacy" tag (and tagging this question as such)? – JMCF125 Aug 30 '13 at 22:56
  • @Gerry, probably, Wikipedia agrees. As you contributed to close, couldn't you either merge these or change the reason for the close? – JMCF125 Aug 31 '13 at 20:52
  • I don't think this should have been closed (oops, I mean "put on hold") unless it were a duplicate, and that was not given as a reason. The question concerns mathematics. Much easier questions (e.g., elementary-school level arithmetic) are asked and answered here all the time and not put on hold. – Stefan Smith Aug 31 '13 at 21:47
  • @JMCF125, you attribute to me powers I don't have. I voted to close as a duplicate, but the majority of voters gave a different reason, and I'm not sure whether even a moderator can change that. Possibly a moderator can merge questions --- what you can do is flag the question for moderator attention and then make your case. Alternatively, you could open a thread on the meta site. – Gerry Myerson Sep 01 '13 at 01:16
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    I temporarily re-opened this question to close.. errr.. mark it as a duplicate. No reopen votes were left orphaned by my actions. IMO (and that of others, it seems) being a duplicate is more of an issue for this question. – user642796 Sep 04 '13 at 13:10

2 Answers2

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The last conclusion is simply wrong. You are right, they paid $27$ dollars altogether. The pens however cost $25$ dollars ($30$ dollars initially, then $5$ discount), so that's the two dollar donation difference.

There is no sense in adding the $2$ dollars, since the nine dollars each friend spent includes the donation.

EDIT: As T. Bongers noted, this is a known fallacy, so you might want to check Wikipedia or google for "missing dollar" for more detailed explanations.

Tomas
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  • I know actual coat is 25 dollars but when you calculate reverse we are only get 29 dollars – Jag Aug 30 '13 at 21:03
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    As I stated, the reverse calculation is wrong. Since the pens cost $25$ dollars, but the friends spent $27$ dollars, this $27$ dollars include the donation, so subtract it, don't add it. Actually, the $30$ dollars are of no relevance, as only $27$ were used. They could even be billionaires... – Tomas Aug 30 '13 at 21:05
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    There is no missing dollar... –  Aug 30 '13 at 21:15
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    Hehe, nice! I did not know that this was that popular, but it's even on - @JAG, check for reference - Wikipedia. – Tomas Aug 30 '13 at 21:18
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10 x 3 = 30. 30 - 5 = 25. 25 + 3 = 28. 28 + 2 = 30. so, no missing $.

stig
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