# Missing dollar riddle
The missing dollar riddle is a classic arithmetic brain teaser in which three guests pay $30 for a hotel room, receive a $5 refund through a bellhop who keeps $2, and are then led through a calculation that appears to show $1 vanishing. No money is actually missing; the riddle works by adding two quantities that should not be added.[1](https://www.mathwords.com/m/missing_dollar_paradox.htm)
| Key fact | Detail |
|---|---|
| Setup | Three guests pay $10 each for a $30 room; the clerk finds the rate is $25 and gives $5 to the bellhop to return[1](https://www.mathwords.com/m/missing_dollar_paradox.htm) |
| The trick | The bellhop keeps $2 and returns $1 to each guest; the riddle then adds the guests' $27 to the bellhop's $2, getting $29 against the original $30[2](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar) |
| Resolution | The $27 already contains the bellhop's $2; the honest ledger is $25 (hotel) + $2 (bellhop) + $3 (refunded) = $30[1](https://www.mathwords.com/m/missing_dollar_paradox.htm) |
| Type of error | A double-counting error: a quantity that should be subtracted is added, producing a sum with no meaningful relationship to the original total[3](https://www.fantasylabs.com/articles/pearl-jam-the-missing-dollar-riddle-and-the-double-counting-error/) • [1](https://www.mathwords.com/m/missing_dollar_paradox.htm) |
| Earliest print version | R. M. Abraham's 1933 book *Diversions and Pastimes*; the inventor is unknown[2](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar) |
| Family | One of a larger class of mathematical misdirection puzzles, versions of which have been around since at least the 1700s[3](https://www.fantasylabs.com/articles/pearl-jam-the-missing-dollar-riddle-and-the-double-counting-error/) |
## The puzzle as stated
In the standard version, three people check into a hotel room costing $30 and each pay $10. The manager later realizes the room costs only $25 and gives $5 to the bellhop to return. Because $5 cannot be split evenly three ways, the bellhop keeps $2 and hands $1 back to each guest. Each guest has now paid $9, so together they have paid $27, and the bellhop has $2. The riddle asks: $27 + $2 = $29, so where did the missing dollar go?[1](https://www.mathwords.com/m/missing_dollar_paradox.htm) • [2](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar)
## Why no dollar is missing
The question is not a fair one; it is built on a misinterpretation of the situation. The $27 the guests paid already includes the bellhop's $2, so adding the $2 to the $27 counts that money twice. The correct check is $27 = $25 (hotel) + $2 (bellhop), or equivalently $27 − $2 = $25.[4](https://bminhquang.name.vn/en/puzzles/missing-dollar) • [3](https://www.fantasylabs.com/articles/pearl-jam-the-missing-dollar-riddle-and-the-double-counting-error/)
Tracking where every dollar actually sits makes the illusion vanish. The hotel has $25, the bellhop has $2, and the guests have $3 back between them: $25 + $2 + $3 = $30.[1](https://www.mathwords.com/m/missing_dollar_paradox.htm) The riddle's framing steers the solver toward the wrong equation, a garden-path framing in which the running total sounds right on the surface but mixes up addition and subtraction.[4](https://bminhquang.name.vn/en/puzzles/missing-dollar) • [5](https://www.mytutorlesson.com/the-missing-dollar-logic-puzzle-explained/)
## Why the trick works
The numbers are chosen deliberately. The apparent discrepancy of $1 is small enough that the reader believes something mysterious happened; when the numbers are changed so the final discrepancy is much larger, the reader no longer feels the pull to hunt for the missing amount.[6](https://www.math.cmu.edu/users/math/jmackey/summer/bws_book.pdf)
Marcel Danesi, a professor of semiotics and anthropology at Victoria College, University of Toronto, who writes on puzzles, describes the missing dollar puzzle as a classic of the genre that confounds first-time solvers, with the trap lying in the way the information is presented rather than in the arithmetic itself.[2](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar) The puzzle belongs to a family of mathematical misdirection problems that exploit how people process numerical information.[7](https://trivcentral.com/missing-dollar-riddle-explained/)
## History and variations
The inventor of the puzzle is unknown. The earliest version Marcel Danesi was able to locate was published by R. M. Abraham in his 1933 book *Diversions and Pastimes*, making Abraham the most likely originator, though he notes he stands to be corrected.[2](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar) Versions of this class of mathematical misdirection puzzle have been traced to at least the 1700s.[3](https://www.fantasylabs.com/articles/pearl-jam-the-missing-dollar-riddle-and-the-double-counting-error/)
## Use in teaching
Teachers use the puzzle to show students how to track the directional flow of numbers and distinguish assets from liabilities, a foundation for algebra, accounting, and financial literacy.[5](https://www.mytutorlesson.com/the-missing-dollar-logic-puzzle-explained/) A Carnegie Mellon problem-solving course assigns it as an exercise in carefully keeping track of where all the money ends up: the clerk has $25 in the cash box, the bellhop has $2 in his pocket, and the three guests have $1 each.[10](https://www.math.cmu.edu/~bkell/21110-2010s/homework-1-sol.pdf) The same double-counting structure appears outside recreation as well; commentators have noted that accounting fraud and loss concealment can be viewed as sophisticated versions of the missing dollar riddle.[11](https://kenji.blog/en/p/missing-dollar/)
## References
1. [Missing Dollar Paradox — Definition, Formula & Examples, Mathwords](https://www.mathwords.com/m/missing_dollar_paradox.htm)
2. [Where is the Missing Dollar? Marcel Danesi, Psychology Today (2009)](https://www.psychologytoday.com/us/blog/brain-workout/200912/where-is-the-missing-dollar)
3. [Pearl Jam, The Missing Dollar Riddle, and The Double-Counting Error, FantasyLabs](https://www.fantasylabs.com/articles/pearl-jam-the-missing-dollar-riddle-and-the-double-counting-error/)
4. [The Missing Dollar — Visual Solution, Bùi Minh Quang](https://bminhquang.name.vn/en/puzzles/missing-dollar)
5. [The Missing Dollar Logic Puzzle Explained, My Tutor Lesson](https://www.mytutorlesson.com/the-missing-dollar-logic-puzzle-explained/)
6. [Everything You Always Wanted To Know About Mathematics (CMU, J. Mackey)](https://www.math.cmu.edu/users/math/jmackey/summer/bws_book.pdf)
7. [The Truth About the Missing Dollar Riddle Explained, Triv Central](https://trivcentral.com/missing-dollar-riddle-explained/)
8. [The Missing Dollar Puzzle, James D. McCaffrey (2019)](https://jamesmccaffreyblog.com/2019/05/08/the-missing-dollar-puzzle/)
9. [Funday Times: Missing dollar puzzle, Sunday Times (Sri Lanka)](https://www.sundaytimes.lk/250209/funday-times/finalpage.pdf)
10. [21-110 Problem Solving in Recreational Mathematics, Homework 1 solutions, Carnegie Mellon University](https://www.math.cmu.edu/~bkell/21110-2010s/homework-1-sol.pdf)
11. [The Missing Dollar Riddle: Learning Logical Thinking and Accounting Basics, kenji.blog](https://kenji.blog/en/p/missing-dollar/)
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*Topic: Encyclopedia › Sports, games, and recreation › Board, card, and puzzle games › Puzzles › Physical, logic, and word puzzles › Classical mathematical puzzles*
*Initially written Sep 17, 2026 · Reviewed: Oct 21, 2026 · Edited: Oct 15, 2026; Oct 21, 2026 · Last review: Oct 21, 2026*
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