FOFC Highlander 5/25/06--ZIPs

[Wolfpack]

Welcome to today's highlander game.

Today, we'll have some fun with ZIP codes. We will draw five numbers (0-9) at random. If the five numbers match a ZIP code, we have a hit, otherwise a miss. The challenge will be how many draws will it take before we draw 10 unique ZIP codes. ZIP validity will be based on the USPS website's ZIP lookup feature.

For example: a five-number draw is made that reads "26922". The USPS says this is not a code, so this is a miss and we re-draw. "90609" comes up, and this matches the code for Whittier, CA, so we have a hit.

As it is almost noon EDT, I'll hold this game open until 8 PM tonight.

Highlander winners to date:
Chas in Cinti #4 (5/18/06)
Pumpy Tudors #2 (5/16/06), #6 (5/23/06)
Toddzilla #5 (5/20/06)
wbatl #1 (5/15/06)
Wolfpack #3 (5/17/06), #7 (5/24/06)

[BrianD]

I'm in.

[Passacaglia]

Do we get to know how many ZIP codes there are?

[Wolfpack]

Do we get to know how many ZIP codes there are?

I don't even know that, to tell you the truth.

[Chas in Cinti]

You forgot to put the winner history, etc. in the first post... for shame!

Regards,
Chas

[Raiders Army]

Do we get to know how many ZIP codes there are?
I would guess somewhere between 1 and 99,999. Excluding the additional four of course.

[Abe Sargent]

Neat!

-Anxiety

[Wolfpack]

You forgot to put the winner history, etc. in the first post... for shame!

Regards,
Chas

Added. Happy now to see your name up there? :)

[gstelmack]

I would guess somewhere between 1 and 99,999. Excluding the additional four of course.

I'm pretty sure it's higher than that. I've had at least 5 different ones in my lifetime, so it's actually somewhere between 5 and 99,999.

[BrianD]

I'm pretty sure it's higher than that. I've had at least 5 different ones in my lifetime, so it's actually somewhere between 5 and 99,999.

The instructions claim that 26922 isn't valid, so it is really somewhere between 5 and 99,998.

[Chas in Cinti]

Added. Happy now to see your name up there? :)

Ummm... me? heheheh

YES!

[wbatl1]

I have truly no idea, since I have no idea how many zip codes there are, so mine is a completely random guess.

[Toddzilla]

Since guessing is closed, I'll post my thoughts...

If we assume that out of 20 possible zip codes, 1 is invalid, then we give ourselves a 19:20 chance to hit a legit zip.

So our odds of getting the 10 in a row we want is (19/20)^10, or (.95)^10.

That equals .5987 --- call it 60%.

So if we have a 60% chance to run fof 10-in-a-row, and only a 5% chance to stop the streak on each draw, is there a formula that gives the expected number of chances before we hit 10?

[Toddzilla]

Dola - this doesn't take into account the "miss" that occurs when we draw the same zip code twice inside of ten guesses - since they have to be unique.

Those odds are:

1:10000 (for the second zip code)
+
2:10000 (for the third zip)
+
...
+
9:10000 (for the 10th zip)
equals
45:10000 = 0.45%

so there is 0.45% additional chance of failure.

[Wolfpack]

The appointed hour has passed and the entries have been made. Overall there were 17 entries. On with the draw:

1: 12884--Victory Mills, NY (1 hit)
2: 44578--Miss
3: 35455--Miss
4: 14464--Hamlin, NY (2 hits)
5: 11646--Miss
6: 60541--Newark, IL (3 hits)
7: 82808--Miss
8: 88940--Miss
9: 22594--Miss
10: 95538--Crescent City, CA (4 hits)
11: 65449--Cook Station, MO (5 hits)
12: 59787--Miss
13: 22765--Miss
14: 72454--Piggott, AR (6 hits)
15: 67775--Miss
16: 50265--West Des Moines, IA (7 hits)
17: 91722--Covina, CA (8 hits)
18: 51201--Sheldon, IA (9 hits)
19: 28482--Miss
20: 57032--Harrisburg, SD (10 hits)

So, it took 20 draws to find 10 real ZIP codes. None of the 17 entries had this one right, but they were all around it (aside from a couple of outliers). In the end, Mustang wins it with his guess of 19. Congratulations, Mustang!

[Wolfpack]

BTW, one website I saw said that there were about 43,000 ZIP codes in use, so slightly under half the numbers available from 00000-99999. That means the hit rate was slightly higher than expected (50%).

[Toddzilla]

I'm a stupidass - I thought we needed 10 in a row. EGADS.

[BrianD]

BTW, one website I saw said that there were about 43,000 ZIP codes in use, so slightly under half the numbers available from 00000-99999. That means the hit rate was slightly higher than expected (50%).

I found that website as well, but I wasn't going to tell anyone until after the drawing. I thought my guess of 25 would take the prize. I keep getting close....which means nothing in the world of highlander.

[Abe Sargent]

Congrats!


-Anxiety

[Mustang]

I'll be.. I actually won one of the little contests for once. I'll have to think of something good on the way to work...

[Chas in Cinti]

Hmmm... I guessed 18, I'm feeling pretty good... as I used math too!

(Actually have a BA in Mathematics with an emphasis on Stat and Prob... too much gambling in college... :) )

Regards,
Chas

[Passacaglia]

No fair! Stupid people who actually do research! :-P