Making Change

Roland Piquepaille writes "There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 10 cents, and 25 cents. But is it the most efficient way to give back change? This Science News article says that a computer scientist has found an answer. "For the current four-denomination system, [Jeffrey Shallit of the University of Waterloo] found that, on average, a change-maker must return 4.70 coins with every transaction. He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents." He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. Check this column for more details and references." The paper (postscript) is online.

I hate math...

[Swannie]

I think the advantage to having a 10-cent piece is that it makes the math easy. Let's face it; can you imagine the average cashier at WalMart giving back 98 cents change with an 18-cent coin?

Swannie

Yeah Right...

[IpsissimusMarr]

Are you kidding me?!

Have you ever gotten a bill for dinner for say $12.50 and you give the cashier $15 saying the tip is included?
You would think 15.00 - 12.50 is doable right?

HELL NO! The cashier pulls out a calculator to do the math so she can write it in for the waiter's tips!!!

If people can't add things like this 18cent coins are out of the question.


Although I would like to hear a cashier go,
"That makes $0.88 change sir." Pick out two quarters then, ... *pause* .... and just stare blankly at the change drawer.

D'oh!

[aitala]

Is it too early in the morning or does this article not make sense? I have never seen an 18 cent piece in circulation n the US...

18 cent coin??

[Anonymous Coward]

My God...have I been playing Everquest that long?

Re:Forget it.

[Ripplet]

Exactly. All you need is a 1 cent coin, and a, er, zero cent coin!

4 coins?

[xchino]

"There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 18 cents, and 25 cents"

Where is this 18 cent coin? Have I been living under a rock? Are my dimes now worth 18 cents?

Ah the new math.

[SphynxSR]

I had 18 cents everytime I heard that.

Re:I hate math...

[Anonymous Coward]

Well, I can certainly imagine that. Let's see, 98 cents, that's two 40ct pieces and one 18ct piece. Easy.

The quarter is hard enough

[charlieo88]

I was at a conveinece store yesterday. The price came to $1.37. I tendered $2.12. The cashier's head almost exploded.

87 cent Loony?

[JohnnySkidmarks]

Here in Canada the only chance of our coinage being worth 87 cents is if the US keeps up it's foreign policy for another 6 months. (our dollar hasn't been this high in about 7 years)

Yeah, right...

[Frightened_Turtle]

So- you have 7 18-cent coins, Susie gives you 13, and you give Bobbie 3. How many nickels must Daddy give you for your 18-cent coins...?

Then, you get on a train in Boston traveling east at 300 MPH. In 30 minutes, will you really care about how many 18-cent coins you're carrying?

Re:18 cent dimes?

[ClippyHater]

On e-bay, with a good enough of a write-up and screenshots galore, I bet you could even get $1 for a dime!

Re:D'oh!

[Trailer Trash]

Is it too early in the morning or does this article not make sense? I have never seen an 18 cent piece in circulation n the US...

I'm waiting to see if Taco screws it up in the dup tomorrow, too...

MDC

Re:The quarter is hard enough

[LPetrazickis]

As someone who used to work in a similar establishment, let me just say that I hated people like you.;)

And I like math.:P

Re:Yeah, right...

[d_lesage]

If you get on a trin travelling *east* from *Boston*, it's going to take you a hell of a lot less than 30 minutes not to care. You're more likely to care about the lack of oxygen.

Re:Instead...

[aborchers]

So getting rid of marketeers would *also* simplify making change? What are we waiting for?!

Re:Yeah Right...

[ip_vjl]

One time at a grocery/conveneience store, I had a total come to something like $1.87

Wanting to minimize some of the change in my pocket, I gave the clerk $2.00 in bills and 12 cents.

The clerk tried to hand it back, saying "it's only $1.87"

I said, "yes, but this way, I'll get a quarter back in change."

He took the money, punched it into the cash register, and as he handed me back the quarter, he said "How did you know that?"

It's funny (in a VERY sad way) that to him, the cash register was this magic oracle that told him what to do, and that it didn't occur to him that what he was doing was even knowable without its use.

Re:I hate math...

[Xzzy]

> or some asshole has been *criminally* negligent in
> copy/pasting those coin values

You forgot option three, you didn't read the article. ;)

18, it's a magic number.

[MexicanMenace]

Don't y'all remember the SchoolHouse Rock about counting by 18?

*taps foot*

Eighteen is a magic number.
Yes it is, it's a magic number.
Somewhere in the ancient, mystic eighteenity
You get eighteen as a magic number.
The past and the present and the future,
Faith and hope and charity,
The heart and the brain and the body
Give you eighteen.
That's a magic number.

18, 36, 54 . . .
72, 90, 108 . . .
126, 144, 162 . . .
180.

Preposterous

[syle]

An 18 cent coin is a good idea, but it's only a start. What we really need is one coin per possible amount of change. That way, when you pay with $1.00 for a $0.63 candy bar, you just get one 37-cent coin in return.

This approach simplifies all transactions to one-coin change. Some people might argue that this is just too many coins to keep track of, but since no one keeps track of their change anyway, it wouldn't matter. It's easier to use the new change to pay as well: Instead of $0.67 being 2 quarters, a dime, a nickel, and 2 pennies, it can be paid in one coin. Or, you could use a 50-cent and a 17-cent piece. Or two 27s and a 13! The possibilities are endlessly easy!

Some people say that it's a problem to differentiate the 99 different coins (95 new coins) by sight. There's a simple answer to this -- each coin would have a number of sides based on its amount. A 4-cent coin is a square, an 8-cent is an octogon, and so forth. So, remember, don't give them three quarters -- just reach into your pocket, feel for the coin with 75 sides, and hand it over.

Oh, and if you can't tell a 99-sided coin from a 97-sided coin by sight, perhaps you should stick to smaller denominations.

The new two-cent coins are easy to lose, so be careful.

Re:4 coins?

[Tumbleweed]

> Have I been living under a rock? Are my dimes now worth 18 cents?

Apparently so. That's what your dollars are now worth. :)

Re:Instead...

[Anonymous Coward]

Since we are so concerned with the amount of coins that a cashier has to count, why not just make a separate coin for every whole number between 0 and 100. That way a cashier only has to return an average of 1.0 coins/transaction.

Yeah, haven't you heard about them?

[WIAKywbfatw]

ummm..18 cent coin? hmm...somehow I missed that one :).

Didn't you get the email? Just as the $20 bill is being replaced with a new design, the 10 cent coin is being phased out in favour of a 18 cent one.

This has advantages and disadvantages:

Advantages:

• The new coin has exactly the same appearance as the old 10 cent coin that it's replacing. This makes it both easier to recognise and use in vending machines. Oh, and they can still use the same mint presses too.
• The new coin gives you 80 percent increase in buying power over the old one, overnight and in the same form factor. Moore's Law, watch out!
• No need to ask the boss for a raise, because everyone has more money to spend.
• NFL defensive coordinators need never have to watch game film again! The new improved dime defense allows an extra eight defenders on the field of play, making the passing game obsolete and taking the game back to the I-wing formation era. Extra bonus: wide receivers are rendered useless once more, and Randy Moss and Terrell Owens finally have to shut their mouths and join the rest of us in the real world.

Disadvantages:

• Not everyone recognises the new coins straight off the bat. Some people still insist that they are only worth 10 cents. Don't let them shortchange you! Demand your 18 cents worth!
• Base 18 is a bitch.

By the way, I'll soon be selling shares in my new e-venture: www.boyhaveigotabridgeforyou.com. Sign up now before the stock rockets!

Re:I hate math...

[tmasman]

Could you imagine trying to get change for a dollar?

Customer :Can I get change for a dollar?
Cashier :Would you like,

• 3 x .29, 2 x .05, & 3 x .01
• 2 x .29, 2 x .18, 1 x .05, & 1 x .01
• Oh dear GOD!!!

Yeah, I can see your local fastfood cashier doing that math in their head.
But I'll give him this much... He'd save us 0.81 of a coin each time we got change!
(I don't want 81% of a coin!!! It wouldn't roll or spin so well after you cut it!!!)

Re:A $0.18 coin?

[Art_Vandelai]

A Canadian quarter is worth about 18 cents. Just use those.

Re:The quarter is hard enough

[asmithmd1]

Here is a true story [digiserve.com] about someone who almost got arrested for trying to buy a burrito with a $2 bill. A mall security guard actually helped out.

And in other news....

[nochops]

...In other news today, hot chicks around the world were see smiling, knowing secretly that this guy is never, ever gonna get laid.

Am I retarded?

[medscaper]

The price came to $1.37. I tendered $2.12.

Uhhh...did anyone else have to use a calculator or pencil for this one and go, "Oh, I get it. Those idiot cashiers."?

...snicker...

Re:D'oh!

[crazyphilman]

I think you can file this article in the "most useless use of research resources ever" category. Whoever this Waterloo guy is, he REEEEALLLY needs to get a new hobby.

18 cent coins? 4.70 coins per transaction? Give me a break. I was a geek growing up and even *I* feel like smacking this guy.

Re:Pet peeve

[daeley]

I suck at addition. Give me a theorem to prove!

OK, prove that adding 2,381,240 to 128,037 is the same thing as adding 128,037 to 2,381,240.

Oh, and what is 20% of $12.96? I gotta tip the waitress here. ;)

Re:Pet peeve

[Requiem]

Thm: There exists a dork, such that a dork is you.

Pls. prove. Thanks.

Re:I hate math...

[servoled]

Actually the US does have an 18 cent coin. It's called a Canadian quarter.

Re:I hate math...

[stinky wizzleteats]

Well, I can certainly imagine that. Let's see, 98 cents, that's two 40ct pieces and one 18ct piece. Easy.

Well, I've got you beat. I can do it in two coins. One fifty-three and seven elevenths coin, and one forty four and four elevenths piece. Voila!

Re:Pet peeve

[Anonymous Coward]

Hmmmm. How about:

There exists a problem in class NP that is not in class P.

That should keep you busy for a few weeks.

Re:Preposterous

[brer_rabbit]

I hope you're joking about having 99 different-shaped objects in your pocket.

I believe he was joking about having 99 different coins. An ideal solution would be to have 100 different coins, and include a zero or "null" coin. Therefore the protocol for every transaction could expect a coin.

Re:I hate math...

[PD]

Considering that the last dude who rang up my sale at WalMart had 9 fingers, I'd say that he'd probably find the 18 cent coin quite natural.

Re:Yeah Right...

[HogGeek]

Take the coins, your missing out on watching the dancer try to pick it up with her ...

Two funny (sad) arithmetic stories

[blahedo]

A few years back, my dad was paying for something, and paid an uneven amount in order to get even change. The clerk looked at the money, sort of shrugged, and punched it in and started counting out the change. The catch is---my dad misheard the amount. So when the clerk started counting out a bunch of pennies and nickels, my dad was like, "wait, what?" Had the clerk had *any idea* why my dad had given an uneven amount, she would have realised that he'd misheard the price. But she just punched it in and started counting it out....

A few years after that, my sister (in 5th grade at the time) had a test with a miscalculated grade, and when my mom went in for a parent-teacher conference, she brought it up. In particular, she said she'd added up the number correct and divided by the total number of questions, and got a different percentage... the teacher looked down her nose at my mom and said, "that's *not* how it's calculated." How was it calculated? Well, you have these cardboard discs that you turn according to the total number of questions, and then you read the grade out of the little window corresponding to the number right.... This woman had only the vaguest notion that this grade was a percentage correct, and *no idea at all* that---as a percentage---it could also be calculated by dividing the numbers out. None.

It's one better...

[Graff]

Hey, I can beat this guy at this math thing. According to my calculations there are much more efficient combinations. For example, if you use the coins 1, 2, 4, 8, 16, 32, 64 it will take approximately 3.19 coins per transaction (this is simple binary arithmetic). That's way better than his system which takes 3.89 coins per transaction. The only problem is that the geeks will do just fine with these denominations but just try and ask the average waitress to make change using those coins. Go ahead and ask, I'm sure it will work out just fine! :)

You know, if we mint 1 coin for every amount of change (like a 57 cent coin, a 58 cent one, etc.) then it will only take 1 coin per transaction. Of course then we have to worry about having 99 different coins, making them distinguishable from each other, etc.

The current United States system of currency works just fine. Denominations of 1, 5, 10, 25 are easy enough to calculate and efficient enough for all intensive purposes. Sure this proposed new system may be 17% "more efficient" for a computer but real people need to use the system also.

Some things are best off just left alone...

Re:The quarter is hard enough

[Anonymous Coward]

Along a similar but altogether different line of thought, I know a guy who used to work at a Burger King, and some kid came in once and tried to buy food with a ten dollar bill that was clearly about 50% larger than a normal ten dollar bill, and had only been copied on one side.

Re:I hate math...

[kurosawdust]

Actually the US does have an 18 cent coin. It's called a Canadian quarter. which doubles as the smallest device known to man that makes one reflexively yell "son of a BITCH!" when taken out of their pocket.

OT: was- Re:I hate math...

[bryan1945]

Pennies are worthless?!?!?

Meet my penny-filled sock, my friend! And the sock is stinky, too!

(Gimme a break, it's noon on Friday and I'm bored outta my mind...)-

Re:Two funny (sad) arithmetic stories

[SEWilco]

Well, you have these cardboard discs that you turn...

Yes, I know that some teachers just spin the wheel for grades.

(+1.2, Funny)

Count by 18. Ready? Go!

[jjohn]

<voice style="school house rock">

18...36...54...72...90....108

STOP

Multiply by 18 is like multiplying by 20 but subtracting multiples of 2. So 18*3 is really like 20*3 - 2*3. That's just 60 - 6, or 54! Let's do it again!

18...36...54...72...90...108...126...144...162.. .180!

Ready or not, here I come!

</voice>

no, I didn't use a calculator. I sure hope the math is right.

Re:What we need is widespread acceptance of $1 coi

[anderm7]

Forget $1 coins, I want a $1.0753875 coin so I can buy things that cost 99 cents.

Re:I hate math...

[JayAndSilentBob]

If you have 3 pennies, 4 dimes, 2 eighteens and a dollar, how much should you give the cashier to get the optimal highest single coinage back?

All of it. That really pisses them off, but it works almost every time. I always do that to vending machines. The only time I get screwed is if there are no quarters and I get dimes and nickels back, but that is an unusual case.

Re:I hate math...

[legojenn]

The 18c coin could just be a Canadian Quarter (now that the dollar is worth 72c US).

Re:No, you're not retarded

[mdielmann]

It's just sometimes people like to do this to be helpful or just to be annoying/arrogant (really anticipating the look of panic in the cashiers eyes).

I don't do it for any of those reasons. I mostly do it because I'm lazy and don't want to carry around 5 pounds worth of pennies. Oh, yeah, I also want the only jangling sound when I walk to be from my big brass ones. ;)

Modest proposal

[justfred]

I prefer the following : make pennies worth $1.

This would:

-eliminate the penny,

-give us a distinguishable dollar coin,

-and stimulate the economy

Pennies are visibly and tactilly different from our other coins; can be used in vending machines; are easy to carry around. Plus, Lincoln was a great guy, what with freeing the slaves and all (better than that indian-killer Jackson that's on the $20, at least) and this lets us honor him once again.

Income would be redistributed somewhat randomly to people with big jars of pennies. The ultra-rich (you know, the ones getting the big tax cuts) probably have no more than a handfull of pennies. Some people would chose to hoard the new dollars; while others would spend them with abandon. And wouldn't you like to pay your taxes by sending in several rolls of pennies?

Just for laughs, I'd make "wheat cents" worth $100.

Pennies

[notwhole]

I just failed to find any of my one sided pennies....Curse you third dimension!

Re:Non-decimal systems have advantages

[Anonymous Coward]

>>For example, with 12 ounces in a pound

When did a pound lose 4 ounces? I know ... it must have gone to Jenny Craig or was "Sweatin to the Oldies".

Re:I hate math...

[e2d2]

The only problem with our current monetary system is that inflation has made pennies freakin worthless.

Except for this penny [yahoo.com]

Besides a good roll of pennies and a sock are good for those times you have to dish out some street therapy.

Re:No, you're not retarded

[medscaper]

Oh, yeah, I also want the only jangling sound when I walk to be from my big brass ones.

I don't think those Sacagaweas "ones" are really brass - they just look it.

Sorry. Couldn't resist.

Re:I hate math...

[questor]

It probably doesn't correspond to reality, but the topic of killing penny production came up in some episode of _The West Wing_ over a year ago, and the reason given there that it would never fly was that the chair of a committee the proposal would go through was from Indiana, Lincoln's home state...

Re:Am I retarded?

[rnelsonee]

Nope, only cause I read the earlier post about $1.87, and tendering $2.12. I realized "hey, this guy is getting three quarters back cause the other guy that commented got one back!" :)

Re:Yeah Right...

[Anonymous Coward]

Whitness ye fools the rebirth of the Pi Troll!

3.1415926535897932384626433832795028841971 69399375105820974944592307816406286208998628034825 34211706798214808651328230664709384460955058223172 53594081284811174502841027019385211055596446229489 54930381964428810975665933446128475648233786783165 27120190914564856692346034861045432664821339360726 02491412737245870066063155881748815209209628292540 91715364367892590360011330530548820466521384146951 94151160943305727036575959195309218611738193261179 31051185480744623799627495673518857527248912279381 83011949129833673362440656643086021394946395224737 19070217986094370277053921717629317675238467481846 76694051320005681271452635608277857713427577896091 73637178721468440901224953430146549585371050792279 68925892354201995611212902196086403441815981362977 47713099605187072113499999983729780499510597317328 16096318595024459455346908302642522308253344685035 26193118817101000313783875288658753320838142061717 76691473... and so on...

Re:*whap*

[shreak]

In Canada they have the Loony and Toony (denziens of the maple leaf state, please correct my spelling). These are $1.00CA and $2.00CA coins respectivly.

A friend and I were in CA on business and were totally unable to figure out the stripper tipping protocol. We had a few USD which the ladies were happy to accept. But then we were down to "hard" CA currency.

"Maybe you throw them?" I asked. Of course we didn't want to risk chipping a tooth.

One of the ladies drifted over after a while and started talking. She was from the US and I asked her how it was done. She took a Loony from me and walked up to the stage, put it between her teeth and lay down on her back on stage. The performer at the time crawled up over her, mouth over mons, and crawled backwards and removed the coin with her breasts. Very Hot!

She then gestured me over, obvously expecting me to do the same thing! Having spent some time in US strip clubs, this level of contact is strictly Verboten! Enough to get you ejected into the -30 CA winter air. My friend wasn't so shy and walked up and got the ride of his life!

Canada may be cold in the winter but the ladies can be vary warm!

=Shreak

Re:I hate math...

[Anonymous Coward]

Not watching the markets too closely lately are we? Re-elect G.W. Bush for another term and your 18 cent coin will be the Canadian dime :/

Re:Pet peeve

[swillden]

Oh, and what is 20% of $12.96? I gotta tip the waitress here. ;)

Just put a $50 bill on the table, rub her thigh and raise your eyebrows as if to say "How about it?". When the cops come, ask them what 20% of $12.96 would be.

Re:18-cent is really a red herring - 2-cent works

[Ralph Wiggam]

And you would never have to pay the power company. You could just collide a penny and a negative penny and use the resulting energy to heat your house.

-B

Re:I hate math...

[_ph1ux_]

On one hand?!!!!