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Let's start with a limit on the number of spaces we can use at 8.

 

Add the alphabet, 26 letters upper case and 26 more lower case. 

 

Throw in ten numeric figures from 1 through 9 plus zero, total 10.

 

Require exactly 6 spaces be used for numbers and / or letters.

 

Allow spaces, periods, dashes, slashes, or asterisks for the last 2.

 

Now, how many possible combinations can we have?

 

This is to prove a system I devised to identify tooling for a company I worked for in the eighties.

 

It would have required computers, laser IDs on tools, and bar codes and readers.

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I get 54,419,558,400

 

36^6*5^2

 

36 possible entries in each of the first 6 slots, so 36*36*36*36*36*36

5 possible entries in the last 2, so 5*5

 

Now, if the 2 slots for special characters can be anywhere and not just in the last 2, then it gets higher.  I'd have to think a minute to cipher that out. 

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As I read it, the field is 8 locations.

 

The first 6 can be upper or lower case characters or a digit. So 62 possibilities per location. (Quibble: 0 and O look very similar and both are often pronounced "oh")

 

The last two positions can be one of 5 special characters.

 

Assuming any character can be repeated in the first 6 or last two positions.

 

62*62*62*62*62*62*5*5

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1 hour ago, Forty Rod SASS 3935 said:

Let's start with a limit on the number of spaces we can use at 8.

 

Add the alphabet, 26 letters upper case and 26 more lower case. 

 

Throw in ten numeric figures from 1 through 9 plus zero, total 10.

 

Require exactly 6 spaces be used for numbers and / or letters.

 

Allow spaces, periods, dashes, slashes, or asterisks for the last 2.

 

Now, how many possible combinations can we have?

 

This is to prove a system I devised to identify tooling for a company I worked for in the eighties.

 

It would have required computers, laser IDs on tools, and bar codes and readers.

slashes? Back slash and forward slash? Or just one?
 

By spaces, you mean characters, not space bar which was my first interpretation. The spec should have avoided easily confused characters, I/J, oh/ zero, 1lI (one/ell/Eye), as well as any upper-lower combinations which might be easily confused.  Other responses should be considered an upper limit on the number of reasonable choices.

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3 hours ago, John Kloehr said:

As I read it, the field is 8 locations.

 

The first 6 can be upper or lower case characters or a digit. So 62 possibilities per location. (Quibble: 0 and O look very similar and both are often pronounced "oh")

 

The last two positions can be one of 5 special characters.

 

Assuming any character can be repeated in the first 6 or last two positions.

 

62*62*62*62*62*62*5*5

This is my interpretation.

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Forward slash only, and let's go with numerics where confusion my show up with alphabetics, including lower case letters.  Space without any character means a space bar gap.

 

Upper limits? Our in-house computer geek at that time estimated several million end combinations but he didn't have the means to narrow it down.

 

The locations can be anywhere on the grid of eight locations, but there must be six numbers and the others can be letters or the above mentioned mentioned other characters.

 

And just for what it's worth. I don't want to even see a printout of the final combinations.

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4 hours ago, John Kloehr said:

As I read it, the field is 8 locations.

 

The first 6 can be upper or lower case characters or a digit. So 62 possibilities per location. (Quibble: 0 and O look very similar and both are often pronounced "oh")

 

The last two positions can be one of 5 special characters.

 

Assuming any character can be repeated in the first 6 or last two positions.

 

62*62*62*62*62*62*5*5

 

daggum it I forgot about capitalization.  as you can see i forget about it when i post too. 

 

but now he's changed it up. 

 

1 hour ago, Forty Rod SASS 3935 said:

Upper limits? Our in-house computer geek at that time estimated several million end combinations but he didn't have the means to narrow it down.

 

My number was over 54 billion and it's orders of magnitude too low because I forgot capitalization.  The modfications will make it go even higher because they can be in any position, even if it removes some of the letters like o, O, i, I, and l

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One question I have with this schema is it suggests there is intelligence/meaning behind some of the positions and symbols.

 

If so, the theoretical maximum number of combinations may be many orders of magnitude greater than the number of real-world combinations.

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7 hours ago, John Kloehr said:

One question I have with this schema is it suggests there is intelligence/meaning behind some of the positions and symbols.

 

If so, the theoretical maximum number of combinations may be many orders of magnitude greater than the number of real-world combinations.

Huh?

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I hate problems that keep me awake at night, always have, but ultimately that’s why I got a PhD. No, actually it was because the job market sucked in 1971 so figured I’d go to Graduate School.

 

because the special characters can occur anywhere in the string of characters such that things like ABC/D/EF are possible, the solution multiplies by 8!/6!x2! = 28 (8 factorial, etc).

 

because space is allowed and because it may occur anywhere in the string, the combinatoric result includes too many identical possibilities. I will use # instead of space to illustrate. ABCDEF## is identical to ##ABCDEF and #ABCDEF#, thus the final answer must subtract the number of times this can happen. Seriously, I don’t like ABC#DEF# either.

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6 hours ago, Forty Rod SASS 3935 said:

Huh?

Will you run out of identifiers before you run out of the theoretical "name space"? Is there any special meaning to the position of a character or those special characters (., /, -, *, " ")?

 

I once worked at a place using a purely numeric part number. XXX-XXXX-XX. The dashes were for easy human reading, and not in the database. This gave the company 999,999,999 possible part numbers, they would never run out. Yay! But...

 

The first 3 digits defined a "class" of part.

 

The next 4 digits defined a unique part number within the class.

 

The last two digits defined the part version.

 

First problem came when a part already had 99 versions... And needed revision.

 

The next problem came then a certain class of part had 9,999 parts and a new part was needed.

 

They also only had 999 possible classes of parts. But they only used a few dozen of these.

 

So, instead of having 999,999,999 parts in the space, they really only had 100 possible part numbers when considering versions and 9,999 part numbers within any class of parts.

 

The numbering system logic was baked into the database systems which made any solution to the problem expensive.

 

If there is any intelligence/meaning in the schema, there can be a huge difference between the theoretical and practical limits.

 

 

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Totally random positioning.

 

Start out with 1111AA and go from there.  The non-alphabetical and non-numeric characters were just for emergencies.  None of these said anything about the tool but were an identifier of each tool.  Your system was used and that was the glitch.  As an identifier of an individual tool I didn't give squat, I simply wanted to be able to identify a tool by canning it.  The computer would provide all the rest and provide total history for that individual tool.

 

The tool design and engineering people wanted your system and they could read it like a book.  My supply people only wanted to identify each individual tool and read the bar code to find out what it was and its history and storage location.

 

Our test runs worked perfectly, but the tooling people went nuts and we were proving our system when the company was bought by Lucas Electronics ("The Prince Of Darkness") with the promise that we would all keep our jobs.

 

Five weeks later they brought in their own people and all but a small handful of ours were laid off (read fired).

 

They closed both California plants, moved the operation to Utah, put it in a place with no rail or air transportation and terrible winter driving in a building with flat roofs and skylights in location known for 60-150 inches of snow (the folks at Alta, Brighton, Park City etc. loved that location), and the whole thing went under in about five more years.

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5 hours ago, Marshal Mo Hare, SASS #45984 said:

because the special characters can occur anywhere in the string of characters such that things like ABC/D/EF are possible, the solution multiplies by 8!/6!x2! = 28 (8 factorial, etc).

 

you mean the 1.4 trillion number (64^6 * 5^2) gets multiplied by 28 because the special characters can be anywhere?  So now we're up to 39,760,164,908,800 before taking out the characters that are too similar, like oi1, etc.  Cool.  Can you explain how you figured 28 out?  I racked my brain and I never learned how to deal with anything this complex with this type of math. 

 

5 hours ago, Marshal Mo Hare, SASS #45984 said:

because space is allowed and because it may occur anywhere in the string, the combinatoric result includes too many identical possibilities. I will use # instead of space to illustrate. ABCDEF## is identical to ##ABCDEF and #ABCDEF#, thus the final answer must subtract the number of times this can happen. Seriously, I don’t like ABC#DEF# either.

 

You lost me here.  I must have missed whatever was said about spaces. 

 

After your post he told us the special characters may not be used at all.  Is that what you mean?  That adds more possibilities.  I think that would just make the 5^2 into 6^2.  I'm going to guess 5 characters get removed for being problematic so now we're at 42,517,977,910,128 possible combinations.  Over 42 Trillion. 

 

(59^6 * 6^2 * 28)

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