Rollover next time

[+georgeandmary]

So if it's now base 32, which cache id# will roll it over again? GCZZZZ

 

george

 

Wanna go for a ride?

[robertlipe]

It's actually base 31, with a working set of digits coming from the set {0123456789ABCDEFGHJKMNPQRTVWXYZ} so, yes, all "Z"'s would be the highest representable number. This number would have a value of 31^4, or 882,401 in decimal. However, since the bottom 411,120 units were thrown away to keep compatibility with the 65535 existing caches, that range gets shifted down by 411,120 (don't start me...) so GCZZZZ will have a numeric value of 512,400.

 

At one point, the master plan for the GC universse was going to be base 32, but someone pointed out that it was possible to spell a naughty word, so it was made base 31, thus reducing the domain space from 4^32 to 4^31 before further limits are applied.

[+The Cheeseheads]

quote:

---

...thus reducing the domain space from 4^32 to 4^31 before further limits are applied.

---

 

Maybe I'm misremembering my algebra, but wouldn't it be 31^4 and not the other way around? That gives 1,048,576 (Edit: 923,521... duh!) possible combinations as opposed to 4.6x10^18 which seems a little high.

 

- - - - -

Wisconsin Geocaching Association

 

[This message was edited by Cheesehead Dave on April 25, 2003 at 11:00 AM.]

[+cachew nut]

I saw GCG0AT today. The 0 is the number zero, but it still looks like goat

[Dinoprophet]

quote:

---

Originally posted by robertlipe:

This number would have a value of 31^4, or 882,401 in decimal.

---

quote:

---

Originally posted by Cheesehead Dave:

31^4 and not the other way around? That gives 1,048,576 possible combinations

---

Erm...I get 31^4 == 923,521. Which does give 512,401 as the total number available under the new system when you leave out the 411,120 numbers that were skipped.

 

BTW, why did it go from GCFFFF to GCG0000? Why not GCFFFG? We could have squeezed out 3375 more numbers that way.

 

I can still spell some very naughty words with the letters available, too.

 

(I'm just playin' wit'cha, admins).

 

"Winter's just the curtain. Spring will take the bow"

-- Richard Shindell, Spring

 

[This message was edited by Dinoprophet on April 25, 2003 at 08:17 AM.]

[+Byron & Anne]

This should produce some interesting waypoint names. How many 4 letter words can you think of?

 

Also, is it a 0 or a O. Is it an I or a 1. Could get interesting.

 

Byron

[Dinoprophet]

quote:

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Originally posted by Byron & Anne:

Also, is it a 0 or a O. Is it an I or a 1. Could get interesting.

---

That's why (I imagine) those letters were left out.

 

"Winter's just the curtain. Spring will take the bow"

-- Richard Shindell, Spring

[+Byron & Anne]

The correct math for number of possible waypoints is permutations. The number of permutations for 31 characters taken 4 at a time is 755,160. Of those permutations 65535 were used. That leaves 689,625 left to go. Now there should be something less than that because of the 4 letter words that will pop up.

 

Byron

[mortonfox]

quote:

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Originally posted by Byron & Anne:

The correct math for number of possible waypoints is permutations. The number of permutations for 31 characters taken 4 at a time is 755,160. Of those permutations 65535

---

 

It's more than the number of permutations because you can use more than one of the same digit/letter in a cache ID.

[Dinoprophet]

quote:

---

Originally posted by Byron & Anne:

The number of permutations for 31 characters taken 4 at a time is 755,160.

---

Hmm, we now have *four* different numbers for 31^4.

 

quote:

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Of those permutations 65535 were used. That leaves 689,625 left to go.

---

Correct, but anything less than GCFFFF that also conatins G-Z have been skipped. For example, GCD00G-GCDZZZ will not get used. There are 16 such groups, and (31*31*15) numbers in each group, which means 230,640 numbers go to waste....uh, oh. Now my own numbers are inconsistent with each other.

 

Warm Fuzzies, help!

 

"Winter's just the curtain. Spring will take the bow"

-- Richard Shindell, Spring

[robertlipe]

quote:

---

Originally posted by Cheesehead Dave:

 

wouldn't it be 31^4 and not the other way around?

---

 

Yes, I typed it right in the part I was actually thinking about. The afterthought where I realized I didn't fully answer the original question, I swapped them. I also incorrectly "backcomputed" one of the interim values. Let me try my answer again with hopefully fewer typos:

 

It's actually base 31, with a working set of digits coming from the set {0123456789ABCDEFGHJKMNPQRTVWXYZ} so, yes, all "Z"'s would be the highest representable number. This number would have a value of 31^4-1, or 923,520 in decimal. However, since the bottom 411,120 units (GC0000-GCFFFF) were thrown away to keep compatibility with the 65535 existing caches, that range gets shifted down by 411,120 (don't start me...) so GCZZZZ will have a numeric value of 512,400.

 

The number of caches skipped was not 65535. We're not going to get a GC000G, for example. The entire block from GC[0-9][A-F] was skipped, as in a post explained by Elias.

 

The correct math is not permutations becuase the same digit can be used multiple times.

 

I also answerd the number of english words that cn be computed from this in another post.

[+GrizzlyJohn]

And you know the only thing I can think of is sitting in math class in high school. Falling asleep thinking when in the hell am I ever going to use this stuff. DOH! I guess it is a good thing somebody was paying attention.

[+cachew nut]

Another cool looking GC number.