The Penny Puzzle

[Rob Lister]

For background on this puzzle, see:
viewtopic.php?p=1003576#p1003576

[Regarding pennies] To be honest, I throw them away, right in the parking lot of the store that gives them to me. Yes, littering, ironically. I have no choice. There's not enough room in my car's ashtray (which is helpfully embossed on the interior "Not an ashtray") for pennies, which would eventually build to 4 pennies to every other coin if I allowed them (I think ... there's interesting math there ... I'll have to think about it). But I digress.

Warning, I have no answer to this puzzle but it should be figuroutable.

Ok, setup!

Assume in your daily transactions, you always pay with cash. I know, it strains credibility, but suppose you're Robinson and no bank or card company will deal with you.

Assume you have a large change receptacle in your car (call it gallon size, for fun, doesn't much matter) and you always, always put all your loose coin change in said receptacle.

Assume each and every store clerk logically selects proper coin denominations in giving you change, i.e. they wouldn't give you six pennies in lieu of a nickel and penny.

Assume denominations of pennies, nickels, dimes, quarters only; that half-dollar and dollar coins do not exist, as they almost don't anyway.

Last assumption, assume you're not the type of person to nitpick puzzle wording.

Okay, puzzle!

When the receptacle is full, you dump it out and separate the coins according to their denominations.

What are the ratios of of the differing denominations?

Post your answer but

Spoiler:

spoiler

your work.

[ed]

1 to 4 to 4
Not sure why. Maybe because if it ... it flips over to the next denomination at 5 soooooo "4" is important.

There

[Hotarubi]

I bung it in the machine at the supermarket and I get a shopping voucher.

[Anaxagoras]

When I was little my parents had an old tobacco tin they kept on top of the fridge for coins.. Once I was old enough to reach it, I'd look for quarters and take them out from time to time, so there weren't many quarters. Lots of pennies, nickels and dimes. But mostly pennies. Half dollars were rare in those days. If your change was 75 cents, you'd get 3 quarters. If it was 50 cents you'd usually get 2 quarters.

[Anaxagoras]

Nickels would be the rarest, pennies the most common, I think. Quarters more common than dimes, so ...

For every 200 pennies, I think you'd have 150 quarters, 80 dimes and 40 nickels?

Assuming random distribution.

[shemp]

I'm also assuming the following:

You pay for everything with bills.

You never pull any change out to pay for anything.

Your purchases are price-random; you don't buy a lot of items for the same price or that end with the same decimal amount, like $0.99.

You don't have a wife who raids the jar.

You are not Cheating Cunt Ed.

My calculation with rounding of percentages:

Spoiler:

Of every 470 coins (represents $0.01 through $0.99 once each)
200 pennies, 42.55%
40 nickels, 8.51%
80 dimes, 17.02%
150 quarters, 31.91%

Which is the same as Anax, so he was right.

[gnome]

Assume in your daily transactions, you always pay with cash. I know, it strains credibility, but suppose you're Robinson and no bank or card company will deal with you.

Assume you have a large change receptacle in your car (call it gallon size, for fun, doesn't much matter) and you always, always put all your loose coin change in said receptacle.

Assume each and every store clerk logically selects proper coin denominations in giving you change, i.e. they wouldn't give you six pennies in lieu of a nickel and penny.

Assume denominations of pennies, nickels, dimes, quarters only; that half-dollar and dollar coins do not exist, as they almost don't anyway.

OK so far

Last assumption, assume you're not the type of person to nitpick puzzle wording.

I'm out. :D

[Witness]

Which is the same as Anax, so he was right.

Ditto. Did it by brute force:

https://i.imgur.com/t2RmGxj.png

[Rob Lister]

Nickels would be the rarest, pennies the most common, I think. Quarters more common than dimes, so ...

For every 200 pennies, I think you'd have 150 quarters, 80 dimes and 40 nickels?

Assuming random distribution.

You get credit but -20 points for not showing work.

[shemp]

I didn't really show my work either. I did it in my head. The pennies are obvious, they come into play 1-4 and 6-9 every ten cents, so that's 20 per ten cent range or 200. The quarters are easy too because there's 1 for each amount from 25-49 cents, 2 for each from 50-74 cents, and 3 for each amount from 75-99 cents. The nickels and dimes, you just figure how many there are at 5 cents, 10 cents, 15 cents, etc. then multiply each value by 5.

[Witness]

I see all your coins have cute nicknames. What a touching Love Story™. :BigGrin3:

[Rob Lister]

I see all your coins have cute nicknames. What a touching Love Story™. :BigGrin3:

??? tons for bills, few for coins. two-bits for quarter but that's the only one that comes to mind. Susan B for a dollar coin used to be.

[Anaxagoras]

Nickels would be the rarest, pennies the most common, I think. Quarters more common than dimes, so ...

For every 200 pennies, I think you'd have 150 quarters, 80 dimes and 40 nickels?

Assuming random distribution.

You get credit but -20 points for not showing work.

I worked it out in my head. Wasn't quite 100% sure of the answer, but I guess I should have trusted myself more.