Paying Paradox. Help

Let's say you want to buy a $97 shirt. You borrow $50 from Friend 1 and $50 from Friend 2. You buy the shirt and get $3 as change. You keep $1 for yourself, one for Friend 1 and the other for Friend 2. Thus, making your debt to Friend 1 $49 and Friend 2 $49 If you add the debts, 49+49, it is 98, and then add your $1 which makes $99. Where is the missing dollar?

#Riddles

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

See this as:

By adding the debts, you are calculating how much you owe the 2 friends, which is $\$98$ . This tallies with the amount of money that you have spent or have: $98=97$ (from the shirt you bought) $+1$ (that you kept. )

Happy Melodies - 7 years, 6 months ago

Ok, so lets think about each person separatedly: (You:0 F1:50 F2:50 shop:0) You take the money: (You:100 F1:0 F2:0 shop:0) You buy the shirt (You:3 F1:0 F2:0 shop:97) You give each one 1 dollar (You:1 F1:1 F2:1 shop:97) You pay the debts (You:1-(49+49) F1:1+49 F:1+49 shop:97) (You:-97 F1:50 F:50 shop:97) I dont see any missing dollar.. In your text you dont take the final payment in account to sum all the money :p Actually the sum is always 100 dollars and you'll end up with a -97 debt just as expected. Anyway why are you adding debts? It doesnt have any meaning :P

Lucas Guimarães - 7 years, 6 months ago

You should subtract it.. of course! Instead you are adding it.. :)

Snehal Shekatkar - 7 years, 6 months ago

Very good question, all though, I do not believe it works that way sadly.

Lets think of it another way: Debt is a separate thing from the money itself, it is how much you owe the person. I don't know exactly why it does this with two people, but it seems to not happen with one person only. This is very interesting.

Nick Steichen - 7 years, 6 months ago

By what Logic are you adding the 1$ to the debt of 98$ ???

Santanu Banerjee - 7 years, 6 months ago

This problem is very much like this one.

http://en.wikipedia.org/wiki/Missingdollarriddle

Bat Man - 7 years, 6 months ago

it is with me only...because , from the beginning i don't have any money but bought a shirt with all frnds money. at last i have one dollar with me..thats the missing dollar

Ravindra Sai Durbha - 7 years, 6 months ago

you are supposed to subtract one, not add.

Sharky Kesa - 7 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$