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When I was in college, each semester there were companies that would buy back your used textbooks. One semester I brought my books to the book-buyer, who said "We'll pay you $41". He grabbed a thick stack of one-dollar bills and, with the thumb of his other hand, "buzzed" off a stack of them in about 1 second. He handed them to me. Sure enough, there were 41 one-dollar bills in the stack!

one dollar bills

It took me a year to figure out how he did it so quickly. How did he do it?

HINT:

The bills were new.

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    $\begingroup$ @CiaPan your comment effectively ruins this puzzle, if you could edit out the last part, others might not have the same experience $\endgroup$
    – Joey Harwood
    Commented Feb 2, 2017 at 16:31
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    $\begingroup$ @JoeyHarwood I'm sorry for that. Alas I could not edit the comment, so I removed it. $\endgroup$
    – CiaPan
    Commented Feb 2, 2017 at 19:40
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    $\begingroup$ It's funny how I found this question right after asking a question on Code Golf about counting change. $\endgroup$
    – ckjbgames
    Commented Feb 3, 2017 at 18:59
  • $\begingroup$ Did the book-buyer have any knowledge about what books would be offered to him ahead of time? $\endgroup$
    – Klik
    Commented Feb 5, 2017 at 17:18
  • $\begingroup$ @Klik I believe the book-buyer would have known what books would be offered to him, but there were probably dozens or hundreds of different books, from all the different courses at my 20,000-student college. $\endgroup$
    – BrettFromLA
    Commented Feb 6, 2017 at 17:36

9 Answers 9

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He had gotten them

fresh from the mint/bank in printed order

so that he could easily count the

Serial numbers on them

going up to 41

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    $\begingroup$ Half a second though? $\endgroup$
    – greenturtle3141
    Commented Feb 2, 2017 at 4:09
  • $\begingroup$ @greenturtle3141 "Half a second" was an exaggeration. I wanted to emphasize that the book-buyer didn't do any actual counting. $\endgroup$
    – BrettFromLA
    Commented Feb 2, 2017 at 6:01
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    $\begingroup$ Oh. I considered this possibility but rejected it on the grounds that half a second was probably too short for it to work. $\endgroup$
    – Gareth McCaughan ♦
    Commented Feb 2, 2017 at 9:19
  • $\begingroup$ Counted in a jiffy, this time literally :) $\endgroup$
    – ABcDexter
    Commented Feb 2, 2017 at 11:34
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    $\begingroup$ I want to like this answer, but if you've ever worked with new $1 bills, you know how much they stick together XD $\endgroup$
    – Kenneth K.
    Commented Feb 3, 2017 at 11:10
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This was actually done by

Simply counting and pre-bundling dollar bills in stacks of seemingly random amounts such as 41. The buyer would then name one of those numbers as his quote for any book that reached his counter, grab the corresponding stack from his drawer, and buzz through it as described above to create the illusion that he is an extremely proficient money-counting machine.

Why the effort, you ask? Well, the buyer obviously

hoped that his little stunt would one day be noticed, admired, and eventually recorded in the annals of history via sites such as this one.

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    $\begingroup$ Your answer has 41 upvotes! $\endgroup$
    – fartgeek
    Commented Apr 11, 2023 at 14:14
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Suppose the bills are

in "sub-stacks" of, say, 10, each stack slightly sheared so that a small thumb movement releases 10 bills at a time. (For an exaggerated picture of the geometry I have in mind, imagine a vertical stack of Zs.)

Then the book-buyer could

"count" off four blocks of 10 almost instantly, and then change the angle of "buzzing" to get one more bill. He'd have been markedly slower if he'd been paying you \$49 instead of \$41.

(I don't find this answer terribly convincing and suspect there's something subtler afoot.)

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  • $\begingroup$ that z thing is the only trick I could think of. But considering the hint, I assumed it was something else. $\endgroup$
    – stack reader
    Commented Feb 2, 2017 at 2:11
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    $\begingroup$ If only you were a stack counter instead of a stack reader, you would surely know the answer! $\endgroup$
    – Gareth McCaughan ♦
    Commented Feb 2, 2017 at 2:18
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    $\begingroup$ Very clever! But I don't think that's The Answer. $\endgroup$
    – BrettFromLA
    Commented Feb 2, 2017 at 6:02
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    $\begingroup$ I use this system myself. It makes it trivial to do the job. Buzzing new bills by serial number assumes that you either have an infeasible amount of faith that your bills came direct from the mint with no removals or reordering, or that you previously took the time to verify it. Either is impractical. $\endgroup$
    – Dewi Morgan
    Commented Feb 2, 2017 at 20:25
  • $\begingroup$ This was my guess. It also doesn't require the bills being new. $\endgroup$
    – einpoklum
    Commented Feb 5, 2017 at 19:44
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If the value of the book would always be 41 dollars you could precount your stack of 41 with the last bill facing the other way. when you thumb through and encounter the backwards bill you know thats the 41st bill. This isn't the accepted answer but something I actually did when I was a teller.

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Don't banks give any assortment of bills in totals of 50 dollars? It'd be easy to skim through them until he saw nine left and then hand you the 41. Especially if he is working there and and is handling those 50 stacks often, it'd come pretty quickly to be able to do that sort of thing.

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I tried this myself, and it's much easier with clean bills that line up.

He counted them by ear.
By flicking through each of the bills from top to bottom (buzzing), he can hear each note as it flicks off his nail. Then, due to the amount of practice he has with this, he knows about when to stop. Like someone counting the number of shots from a machine gun.

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    $\begingroup$ The idea is good, but since the lowest frequency human ear can detect is about 16 Hz, counting more than 16 flicks per second - or even less - would be more like a continuous buzz than isolated flicks. Therefore, you would need a few seconds to count 41 bills this way. $\endgroup$
    – Pere
    Commented Feb 3, 2017 at 11:03
  • $\begingroup$ "he knows about when to stop" is the problem in this answer. Its not "about" when to stop. Its exactly when to stop. Perhaps this was what is meant but when I read this it sounds like this trick will get you within a few which doesn't really help when paying people. $\endgroup$
    – Chris
    Commented Feb 3, 2017 at 15:17
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    $\begingroup$ @Pere "the lowest frequency human ear can detect is about 16 Hz" This is totally irrelevant; each flick could be a Khz, hearing 16 instances of these "flicks" in a second wouldn't be much of a problem. Consciously counting these would be hard, if not impossible, but with enough practice you could develop a good 'feel' of the number of bills you flicked through. Point I'm trying to make is that "the lowest frequency human ear can detect" is totally irrelevant in this. There will be some point where it's hard to distinguish individual 'flicks' but it will be (much) higher than 16. $\endgroup$
    – RobIII
    Commented Feb 3, 2017 at 16:07
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    $\begingroup$ ...and to expand on my previous comment: the "lowest" number of flicks a 'human ear' could hear would actually be 0 (or 1 if you want to be pedantic in wether there's a flick or not) per given period (maybe a second, maybe a century). If anything there's an upper bound, not so much of a lower bound. $\endgroup$
    – RobIII
    Commented Feb 3, 2017 at 16:10
  • $\begingroup$ @RobIII The frequency is not directly involved. Anyway, the number of flick a human can tell apart in one second is a lot smaller than 16. The point here is that nobody can count 41 flicks in one second - no matter how well trained. 16 Hz was given just as a matter of comparison. $\endgroup$
    – Pere
    Commented Feb 3, 2017 at 17:22
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This isn't a very creative answer but I'll share it anyway.

The notes were somehow partitioned into groups of 10. For example each 10th one had its corner folded in. Skip to the 4th one with the corner folded in and add one more, you've got 41. Alternatively, a little piece of paper (like a post it note) could be used to partition the notes.

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My solution :

A dollar weighs one gram, maybe he had a balance ? And it showed 41 grams.

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  • $\begingroup$ The OP didn't say anything about him weighing it $\endgroup$
    – MCMastery
    Commented Feb 3, 2017 at 19:25
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    $\begingroup$ To be fair, the OP tagged this puzzle as "lateral-thinking", and didn't say that they didn't weigh it. It's not an out of bounds thing to consider. $\endgroup$
    – Trevor Powell
    Commented Feb 3, 2017 at 23:39
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Here's my answer...

A new fresh stack of bill is either 25 if wrapped black or 50 if orange. If the stacks as black take 2 and remove 9 bills. If orange just take 1 and remove 9 bills. 50-9 is 41

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