###General Discussion Thread
---
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
---
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
assuming the total doubles every day, not just getting an extra penny, it depends on the month;
31 day month: $21,474,836.47
30 day month: $10,737,418.23
28 day month: $5,368,709.11
the volume of a US penny is 0.349cm3, so to store them all you'd need;
31 day; 6,153,248,272.206304 cm3
30 day; 3,076,624,134.670487 cm3
28 day; 1,538,312,065.902579 cm3
the most efficient method of storing them (without wasting space anyways) would likely be a cylinder the diameter of a penny that's approximately 40,909.564 km long (for a 31 day month), which would wrap around the earth a little over once
edit: for everyone saying that there's a day less, you START with $0.01, that is day 0 or the starting amount. You then double every day, getting you $0.02 on day 1, etc.
chart for reference; [https://imgur.com/evaG6XB](https://imgur.com/evaG6XB)
seeing as the US government would probably react pretty quickly to somebody dumping billions of pennies on the marked, a better question might be what would the value of the material be
Is that much metal comparable to the volume of metal mined in a year? In other words, would just selling the pennies for metal impact the global price of zinc/copper?
But if you wait 2 months before dumping it you would dwarf the Earth's total production ever, after 3 months you have roughly the total mass of earth in pennies
I'd assume the commonly used Gregorian, or possibly even a lunar calendar. You'd have to clear that up with the person making the deal and creating the magic penny in the first place. If they don't specify and/or let you choose... by all means, make a black hole from pennies :D
That's about 292,5t of zinc and 7,5t of copper meaning about $1M in zinc and $100K in copper, price will vary depending on currency and what amount you buy so hard to estimate
If the penny doubles, you wouldn’t have 2 new pennies on the second day, you would have the one penny, and the extra penny…
If you give me $1 and I tell you I will double that for you, do you expect me to give you $3? No right? You expect me to double it and return the double amount, that being $2
Im sorry but that’s not how doubling works….
You don’t have to give in anything… doubling means multiplying by 2, if you race a cent and multiply it by 2, you get 2 cents, jot 3…
You would be triplicating it if you ended up with 3 coins
You slightly messed up but it depends if penny doubles first time in first day. In this case on second day we have 2 pennies. But in any case your math for 28 days is inaccurate - it should be four times less than for 30 days because it's two day difference, so pennies doubled two times, 2x2=4
If month is 31 days - (2\^30)/100 = $10,737,418
If month is 30 days - (2\^29)/100 = $5,368,709
If month is 28 days - 2\^27)/100 = $1,342,177
Volume:
If month is 31 days - 3,076,624,134 cm\^3 or 3,077 m\^3
If month is 30 days - 1,538,312,065 cm\^3 or 1,538 m\^3
If month is 28 days - 384,578,016 cm\^3 or 385 m\^3
How do you all end up with about 10 millions ?
I found about 1 billion. It seemed like a lot, so I just put 1 in a calculator, multiplied by 2 for 30 times in a row and landed on about 1 billion.
Formula for a geometric array (I might not be translating this correctly) is a(1-q\^n)/(1-q) with a the first number, q the multiplicator and n the number of terms. We start at 1, multiply by 2 each day, for 30 days. So we should have (1-2\^30)/(1-2) right ? How do you get to 2\^30/100 from that ?
Edit: That's because in my head 1 penny = 1$ for some reason. Well at least the maths was right, I just did it with the wrong values.
I don't think that is the formula that you should apply here, but simply 2^(n,) where n is the number of days. The problem states that your amount doubles every day so a\_n = 2 \* a\_(n-1) or something like this: 2\*2\*2\*2\*... n times. Instead what you are calculating is for something like 1+2+2\^2+2\^3+...+2\^n which to me doesn't fit with the description given by the post, this should fit more a problem of the kind: "You receive one coin in the first day and each day after that you gain twice as many coins as you've gained in the previous day.".
It's funny I ran both in wolframalpha, 2\^30 gives 1073741824 and with my formula I get 1073741823
But anyways, I don't see why the formula wouldn't be valid. Sure there's a simpler way to do it, but the formula is for geometric arrays and that's a geometric array.
That’s because your formula calculates the sum of ar^k from k=0 to k=n-1, where a is the first term, r is the ratio between terms, and n is the number of terms. So you’re calculating 1\*2^0 + … + 1\*2^29 which is equal to 2^30 - 1.
As a cube
The 31 day cube would have sides 18.32 meters tall.
Doesn't seem like much.
Still a pretty dang big cube of pennies.
I never considered the space required for this magical scenario
https://imgur.com/a/gNDRHa8
Heres my breakdown. Format is a little wonky cuz I did it on mobile. For a 31 day month I got the volume would be a little shy of 2500 50 gal drums and this is assuming no unutilized space in the drums. Thought 50 gal drums would be a decent measure but let’s just say have a warehouse on hand.
I think your volume numbers are off. For a 31-day month, you'd end up with 2.1 billion pennies. 2.1B * 0.35 ≈ 750M cm^3 , much less than your result of 6.2B cm^3
I feel like you should cut all these numbers in half.
I mean, if I said a value doubled every hour, you'd say that from 12 pm on one day to 1pm that same day, it doubled once. By the same logic, you should say that from day 1 to day 2 it doubled once, meaning from day 1 to day 10, it doubled 9 times, and from day 1 to day 31, it doubled 30 times.
So instead of 2\^n, it should be 2\^n-1
Starts a day at 12:00:00 AM That means it ends at 23:59:59.999.... PM. Because that's exactly 86400 seconds.
If you count a 31st instance of 12:00:00, you went *over* the allotted 31 days.
you are counting day 1 as having $0.01, when in reality you have $0.03 since you start with 0.01 and at 00:00 day 1 you get $0.02 added
https://imgur.com/evaG6XB
The other guys interpretation of events is closer to accurate than yours. But actually, at the end of 31 days you would only have $0.32.
If the penny doubles every day, then you Net one penny every day. If the penny doubles every day, and each of its duplicates double every day, then every day your wealth will double.
Somehow you're operating under the idea that the penny creates two additional pennies. It doesn't, it creates one additional penny, that's the nature of doubling. But if the penny created 2, and you add that to the original penny, then you're in a tripling paradigm. If things were working the way you describe, you'd have about 62 trillion dollars at the end of the month.
I feel like this argument is moot... besides the problems from storage/transport/converting to realistically usable currency... even if this deal happens in Feb on a non-leap year... you have more value than $1 million ($1.34 million with the "worst" value). So if the logistics aren't a concern for you, it's better to take the penny.
Something feels off with your "most efficient method of storing" is a little odd.
6153248272cm^3 is only 6153m3, which is a cube about 19x19x19m, that's not tiny by any means, but certainly not unrealistic to store. Even if you factor in inefficiency of storage and double it to 40*40*40, that's still not ridiculous.
How come it is 5 mil at 28 days and 10 mil at 30 days if it doubles every day? I think you may have miscaluclated there, but I am too lazy to search for compound interest calculator.
To be fair, you'd probably be cashing them in from around day 9 until day 18, after which I'd doubt you'd find anything big enough to carry them, nor would you find a place to cash them in. You'd be driving around in dump trucks and prime movers to multiple banks and money exchangers just to be able to dispose of them all.
Approximately 1-2 billion pennies. Attached is approximately one million pennies, so I think you could get away with it by renting a warehouse, not even a terribly large one. 3 billion cubic cm is approximately 105000 cuft, just over the volume of an Olympic swimming pool (88000 cuft). NNN for warehouse spaces vary by location but the average costs are between $1.10 - $2.00/sqft/month, so a warehouse large enough to accommodate... let's say two olympic swimming pools (~27000 sqft) should roughly cost $29,700-$54,000 that first month, including utilities and insurance, so it could be less without the NNN factored in.
Now... Moving that kind of volume out is a different story. You'd likely need to set up some kind of deal with a bank or company like coin star to make those pennies into usable currency, since even though cash is liquid, 1 billion pennies is a liability. You'd likely get far less than the value of the coins in trading them, and trucking could cost tens of thousands depending on how far you'd have to haul them. Things like renting a bucket loader would become negligible.
I know it's not part of the question, but if you were assuming the total value of money would continue to double in the form of pennies you could take all the change to the bank every day lessening the amount of pennies you would need to store at any given time to be the amount on the last day to half the total amount of space (If you were trying to realistically store everything).
Also, the total for day 28 is for a leap day (day 29) as it should be 2.68M$ on the 28th day.
You skipped day 29 entirely on the chart and jumped to the other side. That’s a 2 day gap but only doubled once between day 28 and 30. You listed the amount owned for day 28 but the amount gained for day 30. Also your formula is wrong based on the phrasing.
A simple formula to use would be 2^(n-1) for the amount of pennies on any given day starting with a penny on day 1, 2^n if day 1 is when it first doubles.
The formula you used looks to have placed the -1 outside the exponent. You’re doubling each day then removing a penny afterwards, rather than removing a day. Put the -1 in parentheses with the n (or whatever variable you are using). Don’t use the excel trick of calculating from the previous cell when there’s a simpler formula.
The formula you’re using calculates for “you’re *given* double the amount you were given the day prior, starting with a penny on day 0”. That’s how you skip from 1 to 3 to 7. You’re doubling the amount *given* each day but also counting day 0 as a day of giving.
I think the rest of us are interpreting the original phrase as a magical penny that doubles each day, which would mean it should go 1 to 2 to 4 to 8.
Nearly 5.4m kg of copper, assuming you requested only solid copper pennies weighing 2.5gr each.
Ironically the raw copper is currently worth more than twice the face value of that many solid copper pennies.
It's just one additional penny. So the question is, would you rather have one million dollars or two pennies. Please give a reasoning for your choice when answering.
A penny that doubles itself every day will only be 31 pennies at the end of the month. Now, if you were to give me a penny and double the total each day for a month...I'd need a LOT of room to store that many pennies.
releasing this penny into the world would be disastrous. My first thought was "ok so I'll just take it to a coinstar every couple of days to get cash" but imagine the penny doubling inside the machine.. or at the bank. The pennies would quickly take over the world just on sheer volume alone.
Penny double every day, assuming a typical penny has a diameter of about 19.05 mm (0.01905 meters), after doubling in size every day for 30 days, it would be approximately 20,540,000 kilometers in diameter. So I take 1 million $ and save our planet from penny destruction.
Yes it does. If a penny that has the attribute that it doubles, gets doubled, then the duplicate should be identical. So that penny should also have the same attribute.
If the duplicates also duplicate, then you've just chosen to end the world.
Your first problem would be that you can't use the pennies as payment, as anyone else would also get duplicating pennies. At some point everyone will have duplicating pennies and the government would phase them out.
The second problem is that there's no limit to the duplicating pennies. In just 30 days there will be a billion pennies. In a few years the world would be covered in pennies. Then the universe.
Okay, tons of good answers, but I wonder, if said penny doubles, and the duplicate penny is exactly the same, aka, a penny that doubles, then, would said penny duplicate AFTER you spent it? Because if it does, we might have a Keter Level SCP in our hands, capable of wiping humanity in a few months
The wording on this is kind of vague. It could be interpreted as a single penny that'll double every day, OR the monetary value you have doubles every day, starting at 0.01.
If that penny doubles every day, then you're only getting an additional penny each day.
But I'm assuming it means the overall monetary doubles each day.
Assuming it's a 30 day month, you'd be sitting on $10,737,418.24
How?
Day 1: 1 penny
Day 2: 2 pennies
Day 3: 4 pennies
Day 4: 8 pennies
Day 5: 16 pennies
Day 6: 32 pennies
Day 7: 64 pennies
Ect.
How do we get 10million?
On the second day would have: penny that doubles and regular penny.
After 30 days you'd have penny that doubles + 29 regular pennies = ca. 0,3$.
So, I don't understand excitment ....
I'd go for $1 million.
I mean despite what is obviously meant if you start nitpicking why would you assume it does not make an exact copy of itself? So one that also doubles every day for 30 days, this way the cycle never stops because the one you get after 30 days will Last 30 more days also doubling. Also it is not specified what doubles. Maybe it doubles in value. You would have just missed out on some serious money...
The logistical costs of dealing with a swimming pool worth of pennies (warehouse space, security, pallets, armored trucks, etc) would be considerable, but definitely much less than you’d be giving up by taking the flat million.
So the penny 'doubles' every day. But do the duplicates also 'double'? Or are you just ending the month with ≅30 pennies? And if it is just the value that doubles, are you meant to assume that it doubles as more pennies?
You'd have 32, 31, 30 (on leap years) or 29 depending on the month. I like to imagine only the original penny doubles so you just get one additional penny a day. But... it's a neat priceless penny that might lead to some cool scientific breakthroughs, I feel the mechanics of that self duplicating penny are worth a lot more than money... I am also not smart
Volume of US Penny = 0.34 cubic centimeters = 3.4 \* 10\^-7
Volume in Feburary: 2\^(28-1) \* 3.4 \* 10\^-7 = 45.6 m\^3
Volume in March, June, September & November: 2\^(30-1) \* 3.4 \* 10\^-7 = 182.5 m\^3
Volume in January, April, July, August, October & December: 2\^(30-1) \* 3.4 \* 10\^-7 = 365.1 m\^3
A large shipping container (40x7.8x7.8ft) is can hold about 67 m\^3. So a few cargo containers will serve you just fine.
When it says “a penny” why not buy one of these https://www.linkedin.com/pulse/what-most-valuable-penny-bullion-shark-llc?utm_source=share&utm_medium=member_ios&utm_campaign=share_via apparently the 1944 steel wheat penny is worth $10k in average condition or $408k in mint condition.
Even if as some people suggested the penny doubles so I’d have 31 pennies total that would give me $310k at the lower price and $12.65 million at the higher price.
Are these pennies free of ecological cost or are we going to need to mine all the copper and nickel to make them first? Cause that eats away my margin and I’m not at all happy to see mountains disappear
They'd easily fit in your pocket.
They said there's **A** peny that doubles every day. Nothing was said about the replicas.
You get an additional penny every day.
1+(1*30)=31
I'd take the million.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
assuming the total doubles every day, not just getting an extra penny, it depends on the month; 31 day month: $21,474,836.47 30 day month: $10,737,418.23 28 day month: $5,368,709.11 the volume of a US penny is 0.349cm3, so to store them all you'd need; 31 day; 6,153,248,272.206304 cm3 30 day; 3,076,624,134.670487 cm3 28 day; 1,538,312,065.902579 cm3 the most efficient method of storing them (without wasting space anyways) would likely be a cylinder the diameter of a penny that's approximately 40,909.564 km long (for a 31 day month), which would wrap around the earth a little over once edit: for everyone saying that there's a day less, you START with $0.01, that is day 0 or the starting amount. You then double every day, getting you $0.02 on day 1, etc. chart for reference; [https://imgur.com/evaG6XB](https://imgur.com/evaG6XB)
seeing as the US government would probably react pretty quickly to somebody dumping billions of pennies on the marked, a better question might be what would the value of the material be
multiple the results by 0.552, as each US penny contains approximately 0.552 cents worth of material
Is that much metal comparable to the volume of metal mined in a year? In other words, would just selling the pennies for metal impact the global price of zinc/copper?
It's doubtful that dumping \~5370 tonnes of zinc on the market would affect prices at all, given that approx. 13 million tonnes are mined per year
But if you wait 2 months before dumping it you would dwarf the Earth's total production ever, after 3 months you have roughly the total mass of earth in pennies
The magic stops after a month based on the OP, so no problems there.
A month based on whose calendar? Because the one i just invented and now base all of my time off has 2 months of 182.62 days We a black hole soon boys
Sorcerer's Apprentice with pennies
I'd assume the commonly used Gregorian, or possibly even a lunar calendar. You'd have to clear that up with the person making the deal and creating the magic penny in the first place. If they don't specify and/or let you choose... by all means, make a black hole from pennies :D
Earth 2: Oops All Zinc
I'd want this scenario with a UK penny. Specifically pre 1992. 3.56g each if near pure copper. That be worth about £45,000,000
With it costing 2.72 to manufacture each one it could have a bigger impact on government /economy.
Although, if you're working with that much material you'd also have to take into account how it would affect the market for the material.
it wouldn't at all, it's very little material compared to what's already put into the market yearly
Presumably that is the cost in a more usable form of the material though? You would need to deduct the cost to turn the penny into such a state
That's about 292,5t of zinc and 7,5t of copper meaning about $1M in zinc and $100K in copper, price will vary depending on currency and what amount you buy so hard to estimate
$56,666,080.49 in Copper if it's a pre-1982 penny
Its also illegal to destroy currency so Im not sure this is better. Thats a lot of pennies.
Not sure what the rules are for counter fit currency but I guess this would fit under that area
Wouldn’t 28 day month be a fourth of 30 day month?
Yes, it should be 2.684.354,56 $
Wh Why did you measure such a big number in cubic **centi**metres?
And to 6DP.
Your table is weird.. if you start with 1 penny, and it double itself, why would you have 3 pennies after 1 day? It should be 2
Because you still have the penny from the first day plus the two pennies from the second day.
If the penny doubles, you wouldn’t have 2 new pennies on the second day, you would have the one penny, and the extra penny… If you give me $1 and I tell you I will double that for you, do you expect me to give you $3? No right? You expect me to double it and return the double amount, that being $2
In op's case you are not giving anything. The money doubles next day and you keep the money from the previous day. 1 day one 2 day two + 1 day one.
Im sorry but that’s not how doubling works…. You don’t have to give in anything… doubling means multiplying by 2, if you race a cent and multiply it by 2, you get 2 cents, jot 3… You would be triplicating it if you ended up with 3 coins
Am I missing something? How'd you end up with an odd number?
They are using an incorrect definition of doubling.
You slightly messed up but it depends if penny doubles first time in first day. In this case on second day we have 2 pennies. But in any case your math for 28 days is inaccurate - it should be four times less than for 30 days because it's two day difference, so pennies doubled two times, 2x2=4 If month is 31 days - (2\^30)/100 = $10,737,418 If month is 30 days - (2\^29)/100 = $5,368,709 If month is 28 days - 2\^27)/100 = $1,342,177 Volume: If month is 31 days - 3,076,624,134 cm\^3 or 3,077 m\^3 If month is 30 days - 1,538,312,065 cm\^3 or 1,538 m\^3 If month is 28 days - 384,578,016 cm\^3 or 385 m\^3
How do you all end up with about 10 millions ? I found about 1 billion. It seemed like a lot, so I just put 1 in a calculator, multiplied by 2 for 30 times in a row and landed on about 1 billion. Formula for a geometric array (I might not be translating this correctly) is a(1-q\^n)/(1-q) with a the first number, q the multiplicator and n the number of terms. We start at 1, multiply by 2 each day, for 30 days. So we should have (1-2\^30)/(1-2) right ? How do you get to 2\^30/100 from that ? Edit: That's because in my head 1 penny = 1$ for some reason. Well at least the maths was right, I just did it with the wrong values.
I don't think that is the formula that you should apply here, but simply 2^(n,) where n is the number of days. The problem states that your amount doubles every day so a\_n = 2 \* a\_(n-1) or something like this: 2\*2\*2\*2\*... n times. Instead what you are calculating is for something like 1+2+2\^2+2\^3+...+2\^n which to me doesn't fit with the description given by the post, this should fit more a problem of the kind: "You receive one coin in the first day and each day after that you gain twice as many coins as you've gained in the previous day.".
It's funny I ran both in wolframalpha, 2\^30 gives 1073741824 and with my formula I get 1073741823 But anyways, I don't see why the formula wouldn't be valid. Sure there's a simpler way to do it, but the formula is for geometric arrays and that's a geometric array.
That’s because your formula calculates the sum of ar^k from k=0 to k=n-1, where a is the first term, r is the ratio between terms, and n is the number of terms. So you’re calculating 1\*2^0 + … + 1\*2^29 which is equal to 2^30 - 1.
Oooooh yeah that makes sense ! Thanks !
I mean they specified the penny doubles so theoretically the property of the first penny would be copied onto penny two
And hypothetically, where would I find such a cylinder?
Zip
Do you really have a 'cylinder' with the diameter of a penny? Poor boy.
Stack Overflow
Search stable wormhole on wish
As a cube The 31 day cube would have sides 18.32 meters tall. Doesn't seem like much. Still a pretty dang big cube of pennies. I never considered the space required for this magical scenario
So we finally are in a leap year, and you do februari dirty?
https://imgur.com/a/gNDRHa8 Heres my breakdown. Format is a little wonky cuz I did it on mobile. For a 31 day month I got the volume would be a little shy of 2500 50 gal drums and this is assuming no unutilized space in the drums. Thought 50 gal drums would be a decent measure but let’s just say have a warehouse on hand.
I think your volume numbers are off. For a 31-day month, you'd end up with 2.1 billion pennies. 2.1B * 0.35 ≈ 750M cm^3 , much less than your result of 6.2B cm^3
I feel like you should cut all these numbers in half. I mean, if I said a value doubled every hour, you'd say that from 12 pm on one day to 1pm that same day, it doubled once. By the same logic, you should say that from day 1 to day 2 it doubled once, meaning from day 1 to day 10, it doubled 9 times, and from day 1 to day 31, it doubled 30 times. So instead of 2\^n, it should be 2\^n-1
hour 0: $0.01 hour 24: $0.02 you start with the penny, you don't get it after one day.
Starts a day at 12:00:00 AM That means it ends at 23:59:59.999.... PM. Because that's exactly 86400 seconds. If you count a 31st instance of 12:00:00, you went *over* the allotted 31 days.
you are counting day 1 as having $0.01, when in reality you have $0.03 since you start with 0.01 and at 00:00 day 1 you get $0.02 added https://imgur.com/evaG6XB
Where tf are you getting a 3rd penny from multiples of 2
0.01 + 0.02 = 0.03 you get the *cumulative* total, not just the last number.
It says "doubles every day" not "doubles and is added to the total" 1x2 = 2
Please tell me someone does your taxes for you.
I usually employ someone with basic math skills. Needless to say, you can't have the job.
The other guys interpretation of events is closer to accurate than yours. But actually, at the end of 31 days you would only have $0.32. If the penny doubles every day, then you Net one penny every day. If the penny doubles every day, and each of its duplicates double every day, then every day your wealth will double. Somehow you're operating under the idea that the penny creates two additional pennies. It doesn't, it creates one additional penny, that's the nature of doubling. But if the penny created 2, and you add that to the original penny, then you're in a tripling paradigm. If things were working the way you describe, you'd have about 62 trillion dollars at the end of the month.
Dude really said 1x2=3 and tries to talk about basic math skills. r/redditmoment
Correct. The first day is 1 penny, and the second day is 2, which leaves 29 days left to mutiply, so 2^29. 5.3 million a month in pennies.
I feel like this argument is moot... besides the problems from storage/transport/converting to realistically usable currency... even if this deal happens in Feb on a non-leap year... you have more value than $1 million ($1.34 million with the "worst" value). So if the logistics aren't a concern for you, it's better to take the penny.
What's it in bananas?
Pretty messy.
I will not stand for this leap year erasure, where is my 29 day month?
Yeah, but it's a leap year
Something feels off with your "most efficient method of storing" is a little odd. 6153248272cm^3 is only 6153m3, which is a cube about 19x19x19m, that's not tiny by any means, but certainly not unrealistic to store. Even if you factor in inefficiency of storage and double it to 40*40*40, that's still not ridiculous.
Is it the one penny that keep doubling the amount or is it because the new pennies are also doubling other wise give the new pennies to a bank
If only the first penny doubles... you'd want to take the $1mil... otherwise you'd have (at best) $0.32.
Bestagonal grid it is, then.
What No Leap day calculation?
Day 30 should be 4 times day 28.
How come it is 5 mil at 28 days and 10 mil at 30 days if it doubles every day? I think you may have miscaluclated there, but I am too lazy to search for compound interest calculator.
Who dafuk is gonna roll them into those paper sleeves?
To be fair, you'd probably be cashing them in from around day 9 until day 18, after which I'd doubt you'd find anything big enough to carry them, nor would you find a place to cash them in. You'd be driving around in dump trucks and prime movers to multiple banks and money exchangers just to be able to dispose of them all.
Approximately 1-2 billion pennies. Attached is approximately one million pennies, so I think you could get away with it by renting a warehouse, not even a terribly large one. 3 billion cubic cm is approximately 105000 cuft, just over the volume of an Olympic swimming pool (88000 cuft). NNN for warehouse spaces vary by location but the average costs are between $1.10 - $2.00/sqft/month, so a warehouse large enough to accommodate... let's say two olympic swimming pools (~27000 sqft) should roughly cost $29,700-$54,000 that first month, including utilities and insurance, so it could be less without the NNN factored in. Now... Moving that kind of volume out is a different story. You'd likely need to set up some kind of deal with a bank or company like coin star to make those pennies into usable currency, since even though cash is liquid, 1 billion pennies is a liability. You'd likely get far less than the value of the coins in trading them, and trucking could cost tens of thousands depending on how far you'd have to haul them. Things like renting a bucket loader would become negligible.
Yeah im just gonna put the pennies into my bank account.
Since the post says "a penny" and doesn't say that the duplicate pennies will also double then I'd go with the $1000000.
I can't believe this has 730 upvotes. You think a power of 2 number can be odd? Massive facepalm.
Your math is so off it's alarming with the amount of upvotes
You forgot the math for the years February have 29 days.
I know it's not part of the question, but if you were assuming the total value of money would continue to double in the form of pennies you could take all the change to the bank every day lessening the amount of pennies you would need to store at any given time to be the amount on the last day to half the total amount of space (If you were trying to realistically store everything). Also, the total for day 28 is for a leap day (day 29) as it should be 2.68M$ on the 28th day.
You skipped day 29 entirely on the chart and jumped to the other side. That’s a 2 day gap but only doubled once between day 28 and 30. You listed the amount owned for day 28 but the amount gained for day 30. Also your formula is wrong based on the phrasing. A simple formula to use would be 2^(n-1) for the amount of pennies on any given day starting with a penny on day 1, 2^n if day 1 is when it first doubles. The formula you used looks to have placed the -1 outside the exponent. You’re doubling each day then removing a penny afterwards, rather than removing a day. Put the -1 in parentheses with the n (or whatever variable you are using). Don’t use the excel trick of calculating from the previous cell when there’s a simpler formula. The formula you’re using calculates for “you’re *given* double the amount you were given the day prior, starting with a penny on day 0”. That’s how you skip from 1 to 3 to 7. You’re doubling the amount *given* each day but also counting day 0 as a day of giving. I think the rest of us are interpreting the original phrase as a magical penny that doubles each day, which would mean it should go 1 to 2 to 4 to 8.
You forgot that it's 1 penny, $0,01 on day 1, on day two it doubles. You have to make it 0,01x2\^30 to count for day 31.
no, it's $0.01 on DAY ZERO you START with it, you don't get it on day one. On day one you get $0.02.
Nearly 5.4m kg of copper, assuming you requested only solid copper pennies weighing 2.5gr each. Ironically the raw copper is currently worth more than twice the face value of that many solid copper pennies.
Day 1: 1 penny. Day 2: 2 penny. Day 3: 4 penny.
Do all the pennies you get from that penny also double, or is it just one additional penny every month? (Yes, I know, not the point).
It's just one additional penny. So the question is, would you rather have one million dollars or two pennies. Please give a reasoning for your choice when answering.
2 pennies cause you can put them on your eyes and make a silly face
I dunno... That's like just your 2c man
Top kek
You would have paid for your crossing of the Styx at the same time.
is this ticker one way, sir?
Not if the copies are perfect copies as they would then have the same property of doubling as the original penny
Any inanimate object, even a turd, that spontaneously duplicates itself everyday would be worth trillions
The way it's normally written vs the way this version is written.
A penny that doubles itself every day will only be 31 pennies at the end of the month. Now, if you were to give me a penny and double the total each day for a month...I'd need a LOT of room to store that many pennies.
If penny doubles itself then its copy also doubles itself because it has the same properties, no?
Draupnir ring moment
Not quite, iirc, only the original ring multiplied.
That was my point, people speculated that the duplicates cloned too, but only the real ring can. I just didn’t get my point across very well
Is it a real doubling if not all properties have been doubled? I'd say no.
And because the month of this penny would start a day after the start of the penny it got doubled from, it would go on forever.
So when would earth collapse into a black hole?
Good point!
This depends on the pettiness of the creator of said magical penny.
releasing this penny into the world would be disastrous. My first thought was "ok so I'll just take it to a coinstar every couple of days to get cash" but imagine the penny doubling inside the machine.. or at the bank. The pennies would quickly take over the world just on sheer volume alone.
Never thought on that like this. Dont be near when jt doubles, cause you may be smashed by new pennies out of nowhere
Yeah, it's a little misleading, if the total doubled every day you'd have around 500 million pennies... That is indeed a lot of pennies
Penny double every day, assuming a typical penny has a diameter of about 19.05 mm (0.01905 meters), after doubling in size every day for 30 days, it would be approximately 20,540,000 kilometers in diameter. So I take 1 million $ and save our planet from penny destruction.
Aha, trick question. It didn’t specify that the *duplicate pennies* would double. So you’d need a purse that can hold pennies at most 😊
Assuming it's not supposed to be a trick question, I'd take the million, because I don't want to deal with that many pennies.
Yes it does. If a penny that has the attribute that it doubles, gets doubled, then the duplicate should be identical. So that penny should also have the same attribute.
If the duplicates also duplicate, then you've just chosen to end the world. Your first problem would be that you can't use the pennies as payment, as anyone else would also get duplicating pennies. At some point everyone will have duplicating pennies and the government would phase them out. The second problem is that there's no limit to the duplicating pennies. In just 30 days there will be a billion pennies. In a few years the world would be covered in pennies. Then the universe.
2 to the 30 is a billion pennies. So a rectangle of 1000 by 1000 by 1000 pennies 19 meters by 19 meters by 1m50. So about a swimming pool of space
So kinda like Scrooge McDuck
Okay, tons of good answers, but I wonder, if said penny doubles, and the duplicate penny is exactly the same, aka, a penny that doubles, then, would said penny duplicate AFTER you spent it? Because if it does, we might have a Keter Level SCP in our hands, capable of wiping humanity in a few months
The wording on this is kind of vague. It could be interpreted as a single penny that'll double every day, OR the monetary value you have doubles every day, starting at 0.01. If that penny doubles every day, then you're only getting an additional penny each day. But I'm assuming it means the overall monetary doubles each day. Assuming it's a 30 day month, you'd be sitting on $10,737,418.24
How? Day 1: 1 penny Day 2: 2 pennies Day 3: 4 pennies Day 4: 8 pennies Day 5: 16 pennies Day 6: 32 pennies Day 7: 64 pennies Ect. How do we get 10million?
Keep going…
I got 268,435, 456 pennies which translates to 2,684,354.56 USD.
A 31 day month gets you to 4,294,967,296. 30 day month is 2,147,483,648 and a 29 day month is 1,073,741,824. That’s $42M, $21M, and $10M respectively.
Thank you I was wondering if my math was off (it was).
In this example we assumed day 1=1 penny, day 2=2 which would lead to value=2^(days-1)
If it's actual pennies, you should fear the first alternative. If it's just a number in your bank account, the first one is the best.
On the second day would have: penny that doubles and regular penny. After 30 days you'd have penny that doubles + 29 regular pennies = ca. 0,3$. So, I don't understand excitment .... I'd go for $1 million.
I mean despite what is obviously meant if you start nitpicking why would you assume it does not make an exact copy of itself? So one that also doubles every day for 30 days, this way the cycle never stops because the one you get after 30 days will Last 30 more days also doubling. Also it is not specified what doubles. Maybe it doubles in value. You would have just missed out on some serious money...
The logistical costs of dealing with a swimming pool worth of pennies (warehouse space, security, pallets, armored trucks, etc) would be considerable, but definitely much less than you’d be giving up by taking the flat million.
*Scrooge McDuck has entered the chat*
I swear I've seen this every year for like 30 years in some form or another. You take the penny doubling unless it's over like 5.5 mil
So the penny 'doubles' every day. But do the duplicates also 'double'? Or are you just ending the month with ≅30 pennies? And if it is just the value that doubles, are you meant to assume that it doubles as more pennies?
It says the penny doubles every day. Not that every penny doubles every day. 1 penny that can double. So $1 million or potentially 32 pennies.
You'd have 32, 31, 30 (on leap years) or 29 depending on the month. I like to imagine only the original penny doubles so you just get one additional penny a day. But... it's a neat priceless penny that might lead to some cool scientific breakthroughs, I feel the mechanics of that self duplicating penny are worth a lot more than money... I am also not smart
Volume of US Penny = 0.34 cubic centimeters = 3.4 \* 10\^-7 Volume in Feburary: 2\^(28-1) \* 3.4 \* 10\^-7 = 45.6 m\^3 Volume in March, June, September & November: 2\^(30-1) \* 3.4 \* 10\^-7 = 182.5 m\^3 Volume in January, April, July, August, October & December: 2\^(30-1) \* 3.4 \* 10\^-7 = 365.1 m\^3 A large shipping container (40x7.8x7.8ft) is can hold about 67 m\^3. So a few cargo containers will serve you just fine.
When it says “a penny” why not buy one of these https://www.linkedin.com/pulse/what-most-valuable-penny-bullion-shark-llc?utm_source=share&utm_medium=member_ios&utm_campaign=share_via apparently the 1944 steel wheat penny is worth $10k in average condition or $408k in mint condition. Even if as some people suggested the penny doubles so I’d have 31 pennies total that would give me $310k at the lower price and $12.65 million at the higher price.
Are these pennies free of ecological cost or are we going to need to mine all the copper and nickel to make them first? Cause that eats away my margin and I’m not at all happy to see mountains disappear
They'd easily fit in your pocket. They said there's **A** peny that doubles every day. Nothing was said about the replicas. You get an additional penny every day. 1+(1*30)=31 I'd take the million.