What's My 2013 1$ Trinary Bill Worth, Serial Number G86888828B

to the CCF and the currency forum!

Of course your EXACT serial number is unique

But if you're asking how many trinary serial numbers there can be, then a little math is called for.

First question is how many ways can you pick 3 different digits out of the ten digits 0 through 9? This is a combination problem that you can use the Excel combin function to choose 3 numbers out of 10 numbers. The answer is 120. So there are 120 trinary combinations.

The next question is how many ways can you arrange 3 different numbers into 8 positions, where all three numbers can be used more than once. This is the factorial of the number of positions (8! = 40320) divided by the factorial of the number of each digit used. In this case it's just 1 factorial or 1. So there are 40,320 different ways.

Multiply the two answers together to get the number of different possible trinary serial numbers or 120 x 40,320 = 4,838,400.

There are 99,999,999 possible serial numbers (if you ignore the fact the BEP usually stops at 96,000,000 it makes the calculation simpler) and dividing 4,838,400 by 99,999,999 results in 4.84% of the serial numbers are trinarys, which unfortunately isn't at all rare

Since trinary serial numbers aren't rare, they are typically just worth $1 and are spenders to most people, BUT that doesn't mean you couldn't possibly sell it on ebay and potentially clear more than a $1 after ebay fees, PayPal fees and shipping costs. Check ebay sold listings for a better idea on whether or not this possible to do.

Of course, if you just like the serial number and want to keep it for your personal collection then that's fine to do as well

Somebody else please give a shout out if I didn't do the math right

EDIT: Wasn't positive on the 2nd part and it looks like I DIDN'T do the math right. See below.

I to CCF!

I can see this fetching $10 bucks on ebay with 6, "8's". I've done it, but I've also kept some for my collection. People like, what they like. Good luck!

You did, in fact, do the math wrong.

The number of trinary combinations is indeed 120; but the number of arrangements for each combination is only 3^8=6561 (each of the 8 digits has 3 independent options). So the full product is 120*6561=787320.

Actually, it's a little less, because binary serials are counted 8 times each, and solid serials 36 times each.
There are 10 solid serials, and (by a calculation similar to the above) 45*256-9*10=11430 binary serials (not counting solids), so the actual count is 787320-8*11430-36*10=695520 purely trinary serial numbers.

This means that the chance of getting a trinary (that isn't solid or binary) is 0.69552 percent, or just over one chance in 144. Scarce enough to notice, but too common to actively bother with.
(This obviously doesn't account for the missing numbers past 96000000; if you want, I can try to figure that out too, but the calculation would probably be too complicated to post here.)


That said, it's a lot rarer than that to get six of a kind; there are 10 options for the main digit, 8*7/2=28 options for the location of the two differing digits, and 9*9=81 options for the actual two digits (assuming that they can be the same), for a total of 10*28*81=22680 options (about twice as common as radars or binaries).

So yes, I do expect a six-of-a-kind note to sell for more than face - especially given that the digit appearing six times is 8, which is probably the most popular.

Welcome to CCF.

Your note has an interesting serial number and if I found it, I'd be tempted to keep it. I would not pay anything above face value to own it, but that's not saying that someone else wouldn't. Nusimatically, we tend to see a lot of semi-fancy serial numbers and get asked about values and rarity. Notes like the OPs note are not what I would describe as rare or scarce.

If you like it, keep it.

you're out a buck! keep it, selling however probably wouldn't net a lot of profit....sounds like trade bait at a coin club meeting or show

to the Community!

january1may,

OK I feel somewhat redeemed (but still )

Also with the number of 6 of a kind binary serial numbers as

10C2 = 45
2C1 = 2
8C6 =28

for 45*2*28 = 2,520

Probably more than enough math for now

Excuse me while I dig through the dust and cobwebs for my slide rule.