There is a monster lurking in the back of our cupboards and on top of our dressers. It grows in strength every day and every day we feed it. Soon it will be an unmanageable colossus, a rampaging terror that will break loose and wreak havoc upon our lives. It is the ever-deepening jar of change.
American coinage is mostly useless. Every now and then there’s a half-assed attempt to get rid of the penny, which now costs more to make than the coin is actually worth. It’s useless, it’s worthless, and it’s actually costing us money to make them. The reason we haven’t been able to get rid of this numismatic dingleberry is because it’s got Abraham Lincoln on it, and Lincoln used to fart rainbows so it would be heresy to scrap his coin. When the USA got rid of its half cent in 1857, it was worth somewhere between ten and fifteen cents in today’s money. By my reckoning we can ditch not only the penny, but also the nickel and the dime. They are all just dandruff shaped like founding fathers, weighing down our pockets and wasting our lives.
So what can be done to divest ourselves of this scourge? The smart thing to do would be to take the jar to the bank and let them deal with it, but I have never once seen a coin-counting machine in a bank. My bank only grudgingly employs tellers, and that’s only in some of their locations. A third-party company called Coinstar will take your coins from you, and that’s probably the smart thing to do. But screw it, who ever wanted to do anything the smart way? I say let’s get rid of our change the hard way. I earned it, by Jove, and I’ll spend it.
The first thing to do is sort your coins into separate jars for each denomination so you can access them quickly. Now when you leave the house you can grab some coins to spend on your next transaction. But what coins do you need to grab? What’s the smallest number of coins you need to carry in order to make any amount of change?
I won’t lie, I just looked up the answer online and this is what I found:
| Cent | Nickel | Dime | Quarter |
|---|---|---|---|
| 4 | 2 | 1 | 3 |
The smallest number of coins you can carry is ten: three quarters, one dime, two nickels, and four pennies. Oh, that’s pretty boring. It works, but it’s boring. Meanwhile I still have jars of dimes that I just can’t seem to shift. And what am I flinging all these quarters around for anyway? They’re the most useful coin! We need those for laundry machines and arcade games, and they’re the only coin that’s worth a damn anyway so I intend to sit on a big pile of them like Smaug on a mountain of gold.
So let’s mix things up a bit. What’s the lightest combination of ten coins I can carry to make any amount of change? Here’s the same table, but with weights added:
| Cent 2.500 g |
Nickel 5.000 g |
Dime 2.268 g |
Quarter 5.670 g |
|
|---|---|---|---|---|
| 4 | 2 | 1 | 3 | 39.28 g |
| 4 | 1 | 2 | 3 | 36.55 g |
Heyyo, now things are getting spicy. What’s this new row I’ve added? I moved things around a bit and produced a better combination of coins. The Internet’s answer is actually a dumb one. What they’ve done is counted up the smallest number of coins that makes 99¢, but this ignores the fact that you can carry a combination that makes 104¢ and is nearly three grams lighter. You can still make any amount of change and it’s still ten coins! Bonanza.
But wait, there’s more. We’re still carrying three quarters, damn it, and I want to keep my quarters! What if we don’t care about the number of coins? What’s the lightest combination of any coins I can carry to make any amount of change?
| Cent 2.500 g |
Nickel 5.000 g |
Dime 2.268 g |
Quarter 5.670 g |
|
|---|---|---|---|---|
| 4 | 2 | 1 | 3 | 39.28 g |
| 4 | 1 | 2 | 3 | 36.55 g |
| 4 | 1 | 9 | 0 | 35.41 g |
Well that came out of nowhere. Carrying nine dimes, one nickel, and four pennies (fourteen coins) means we can make any value up to 99¢, we don’t spend any of our shiny quarters, and it’s even lighter than our previous answers. Not only that, but it also means we can spend our low-value coins at a faster rate. The Internet’s mathematicians are optimizing for the wrong thing — this combo gives us speed and efficiency.
The last row of the table should be your baseline. When you leave the house, grab those fourteen coins. But there’s no reason to be a slave to the numbers — if you have more nickels than dimes, then maybe grab some extra nickels. If the pennies aren’t going fast enough, maybe grab nine pennies and forget the nickel. Go crazy with it.
Has any of this been worth my time? Hell no. Would I have been better off just throwing all my change into the bin and eating a cupcake instead? Yes. Yes I would. But would my heart leap and sing and dance if I had taken the easy way out? My heart’s never done any of those things anyway, so I may as well stick it out the hard way and take my Pyrrhic victory out of sheer bloody-mindedness. Eat it, Lincoln, you smug, top-hatted, neck-bearded, rainbow-farting git! I win!