## The Penny Puzzle

Stump your fellow simians.
Rob Lister
Posts: 23535
Joined: Sun Jul 18, 2004 7:15 pm
Title: Incipient toppler
Location: Swimming in Lake Ed

### The Penny Puzzle

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

Spoiler:
ed
Posts: 42485
Joined: Tue Jun 08, 2004 11:52 pm
Title: That Firebrand

### Re: The Penny Puzzle

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
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Joined: Fri Feb 14, 2020 2:12 am
Title: Enchantress
Location: This septic Isle.

### Re: The Penny Puzzle

I bung it in the machine at the supermarket and I get a shopping voucher.
Anaxagoras
Posts: 30342
Joined: Wed Mar 19, 2008 5:45 am
Location: Yokohama/Tokyo, Japan

### Re: The Penny Puzzle

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
Posts: 30342
Joined: Wed Mar 19, 2008 5:45 am
Location: Yokohama/Tokyo, Japan

### Re: The Penny Puzzle

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
Posts: 7409
Joined: Thu Jun 10, 2004 12:16 pm
Title: inbred shit-for-brains
Location: Planet X

### Re: The Penny Puzzle

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:
Which is the same as Anax, so he was right.
gnome
Posts: 25995
Joined: Tue Jun 29, 2004 12:40 am
Location: New Port Richey, FL

### Re: The Penny Puzzle

Rob Lister wrote: Thu May 07, 2020 9:35 am
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
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

### Re: The Penny Puzzle

shemp wrote: Thu May 07, 2020 1:56 pm Which is the same as Anax, so he was right.
Ditto. Did it by brute force:

https://i.imgur.com/t2RmGxj.png
Rob Lister
Posts: 23535
Joined: Sun Jul 18, 2004 7:15 pm
Title: Incipient toppler
Location: Swimming in Lake Ed

### Re: The Penny Puzzle

Anaxagoras wrote: Thu May 07, 2020 11:30 am 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
Posts: 7409
Joined: Thu Jun 10, 2004 12:16 pm
Title: inbred shit-for-brains
Location: Planet X

### Re: The Penny Puzzle

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
Posts: 35689
Joined: Thu Sep 19, 2013 5:50 pm

### Re: The Penny Puzzle

I see all your coins have cute nicknames. What a touching Love Story™. :BigGrin3:
Rob Lister
Posts: 23535
Joined: Sun Jul 18, 2004 7:15 pm
Title: Incipient toppler
Location: Swimming in Lake Ed

### Re: The Penny Puzzle

Witness wrote: Fri May 08, 2020 12:42 am 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
Posts: 30342
Joined: Wed Mar 19, 2008 5:45 am
Location: Yokohama/Tokyo, Japan

### Re: The Penny Puzzle

Rob Lister wrote: Fri May 08, 2020 12:18 am
Anaxagoras wrote: Thu May 07, 2020 11:30 am 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.