# Another mathematical conundrum **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [January 18, 2021, 12:38pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803 "2021-01-18T12:38:12Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![jtur88](https://avatars.discourse-cdn.com/v4/letter/j/e9c0ed/32.png) [@jtur88](https://boards.straightdope.com/u/jtur88)\ **Post date:** [January 18, 2021, 12:38pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/1 "2021-01-18T12:38:12Z")
A street fair is offering six Fairbucks coupons for $5. Or you can opt for 5-for-$4 – a better deal, the bonus is 25% instead of 20%’ You give him a fiver, get a dollar change and 5 Fairbuck. Across the street a bank, to get foot traffic, offers $6 cash for $5 if you ask about an account. You give the hostess a five, and as she reaches for an envelope with $6 in it, you tell her there’s a better deal out in the street. She takes a dollar out of the envelope , hands it to you and says “I’ll match that – Here’s your change, and $5, for your four”. Wait a minute. What happened to my 25%? I still gave her my five and got $6. That’s only 20% ---
**Author:** ![kk\_fusion](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kk_fusion/32/15276_2.png) [@kk\_fusion](https://boards.straightdope.com/u/kk_fusion)\ **Post date:** [January 18, 2021, 12:50pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/2 "2021-01-18T12:50:10Z")
In both cases, you get a return of 6 dollars for an investment of 5. If the street exchanger actually insists on getting a five-dollar-bill, there is no difference. If you can buy for exactly four, the street exchanger’s offer is actually a little better, since at the end of the day you might have exactly four dollars left, which will buy you his offer one more time but not the bank’s. ---
**Author:** ![mikecurtis](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mikecurtis/32/3284_2.png) [@mikecurtis](https://boards.straightdope.com/u/mikecurtis)\ **Post date:** [January 18, 2021, 12:50pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/3 "2021-01-18T12:50:39Z")
It’s a variation of the “missing dollar riddle” > **[Missing dollar riddle](https://en.m.wikipedia.org/wiki/Missing_dollar_riddle)** > > Pages for logged out editors learn more > > The missing dollar riddle is a famous riddle that involves an informal fallacy. It dates to at least the 1930s, although similar puzzles are much older. > Although the wording and specifics can vary, the puzzle runs along these lines: > Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-doll... ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [January 18, 2021, 4:17pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/4 "2021-01-18T16:17:56Z")
5 for 4 vs. 6 for 5 is only a better deal if you can repeat it. If you can only do it once it’s 1 free dollar for anyone with at least 4 (or 5) dollars. Here’s a realistic way of repeating the deal: If you give the street fair guy 20 dollars, you get $25 in coupons. If you instead gave each of three friends a fiver and you each walked in to ask about an account, you would only get a total of $24. ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 18, 2021, 10:03pm UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/5 "2021-01-18T22:03:53Z")
> [@jtur88](#): > > Wait a minute. What happened to my 25%? I still gave her my five and got $6. That’s only 20% No you didn’t - after getting $1 in change, you gave her $4 and got $5, just like on the street. Alternatively; if on the street you gave the fair $5, but ask for $1 in change, you will get 5 Fairbucks. Same deal. > [@naita](#): > > If you give the street fair guy 20 dollars, you get $25 in coupons. If you instead gave each of three friends a fiver and you each walked in to ask about an account, you would only get a total of $24. I don’t believe this is the right comparison - instead you need to give 4 friends $4 each, tell them to go to the bank and ask for the same deal as the fair, just like you did. If the bank won’t do it, insisting on $5 down, than as pointed out in the first reply to the thread, it’s not actually the same deal as the fair. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [January 19, 2021, 12:43am UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/6 "2021-01-19T00:43:33Z")
The bank deal doesn’t really resemble the first. It’s really “prove that you carry $5 cash on you and we’ll give you a free dollar”. Altering exactly how the exchange of money happens doesn’t change that. You would have had to negotiate a different deal in advance (“I only have $4 on me; is that enough?”) to change that. What are Fairbucks coupons worth? If they can be exchanged 1-for-1 with dollars at local businesses, then they’re worth less than dollars, since you can’t spend them at Amazon. So it’s really a worse deal, since at best matches the bank offer (a free dollar), but in practice you may not be able to spend it. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 19, 2021, 1:00am UTC](https://boards.straightdope.com/t/another-mathematical-conundrum/930803/7 "2021-01-19T01:00:11Z")
If the banker wanted to give you a really killer deal, she would have given you $4 change, and then given you $2 for your remaining $1. That’s a 100% bonus!