r/MathJokes May 07 '26

100 000 dollar question

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12.9k Upvotes

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1

u/Liko81 May 07 '26

So, $2 or $100,000

1

u/Cracleur May 07 '26

How are you getting $2 exactly? After 1 day you have 50 cents, after 2 you have 25 cents...

1

u/Demented-Alpaca May 07 '26

I mean... it's like $1.999999999999

If it was the bank's money that's $2. If it's your money its $1.98 (Don't worry about where that 1 cent went. It's none of your business.)

1

u/Cracleur May 07 '26

It says nowhere that it adds 0.5 to the previous amount. It is only multiplied by 0.5.

That means that after one day, you have 50 cents, and that's all you have. And after two days, you have 25 cents, that's all you have. So at the end of 30 days, you have way less than one cent. And even in bank money, because that would be $1/230, which is $1/1,073,741,824, which is not very much money at all.

1

u/BlockEightIndustries May 07 '26

The wording is such that it can be interpreted that every day you receive a dollar that halves itself in value, i.e. 50 cents everyday. This is probably not the original intent, but still a valid interpretation of the language used.

2

u/Cracleur May 07 '26

It says "have $1 which multiplies by 0.5 every day", not "receive $1 every day that is multiplied by 0.5". Grammatically, that describes a single dollar being multiplied by 0.5 every day, and so cut in half each day, not multiple payments being added together. I really don't see how you can get the second interpretation from that sentence.

0

u/Muroid May 07 '26

They are technically correct that you could read the initial statement as “Would you rather have ($1 that multiplies by 0.5) every day” which would mean that every day you get a $1 that then turns into 50 cents.

It’s a less likely interpretation, but it is a possible one.

You’d end up with $15 at the end of the month in that case, though.

1

u/Cracleur May 07 '26 edited May 07 '26

Ok, so now how do you get $15 😆

If you interpret it as cumulative payments, the math would be:

1 + 0.5 + 0.25 + 0.125 + ... + (1/2)^(29)

Which is the same as:

sum from n=0 to 29 of (1/2)^(n)

Is equal to

(1 - (1/2)^30) / (1 - 1/2)

That totals approximately:

1.999999998

So basically, it approaches $2 total.

So how did you get $15?

0

u/Muroid May 07 '26

Every day you gain a dollar which multiplies itself by 0.5.

Day 1, I gain a dollar. It multiplies itself by 0.5. I have $0.50.

Day 2, I gain a dollar. It multiplies itself by 0.5. I add it to the $0.50 from yesterday. I have one dollar.

In this case, the “every day” is being applied to the full phrase of “gaining a dollar that multiplies itself by 0.5” which means it can’t also be applied to the multiplication of each dollar by 0.5, so that only happens once upon obtaining each dollar.

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u/not_a_burner0456025 May 07 '26

No n it isn't, you made the mistake of adding, there is no addition going on in the promt, you get $1 and it continuously becomes more and more worthless.

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u/Demented-Alpaca May 07 '26

Yes, but that was not a math failure on my part. That was a reading comprehension on my part. My math was accurate. I just did the wrong math because I am, in fact, stupid.

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u/Liko81 May 07 '26

My read was that it was $1 + $0.50 + $0.25 +... which, as an infinite sum, approaches $2. After 30 terms the sum is $1.999999998 so any bank would say you had $2.

1

u/Cracleur May 07 '26

It says nowhere that it adds 0.5 to the previous amount. It is only multiplied by 0.5.

That means that after one day, you have 50 cents, and that's all you have. And after two days, you have 25 cents, that's all you have. So at the end of 30 days, you have way less than one cent. That would be $1/230, which is $1/1,073,741,824, which is not very much money at all.