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Count up in a somewhat complex way

Posted: Wed Jan 05, 2011 8:10 pm UTC
by FourTael
So we have hex. We have binary. We have base 110. How could I make it more complex?

By changing the bases dependant on the digit.

The base will be (distance from decimal place + 1). So the ones place will count up in base 2, the tens place will be base 3, the hundreds will be base 4, etc.

Here's an example of the first ten posts:

1
10
11
20
21
100
101
110
111
120

etc.

I shall start:

1

Re: Count up in a somewhat complex way

Posted: Wed Jan 05, 2011 9:05 pm UTC
by LucasBrown
And I shall skip to 11, since you have so kindly put the first bundle up. To aid in this, let's put the number in base 10 in parentheses after the multibase number:
121 (11)

Re: Count up in a somewhat complex way

Posted: Wed Jan 05, 2011 9:08 pm UTC
by FourTael
Very well.

200 (12)

Re: Count up in a somewhat complex way

Posted: Wed Jan 05, 2011 10:30 pm UTC
by LucasBrown
201 (13)

Re: Count up in a somewhat complex way

Posted: Wed Jan 05, 2011 10:37 pm UTC
by FourTael
210 (14)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 1:03 am UTC
by LucasBrown
211 (15)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 2:26 am UTC
by FourTael
220 (16)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 3:41 am UTC
by LucasBrown
221 (17)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 4:10 am UTC
by FourTael
300 (18)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 5:08 pm UTC
by APolaris
Wasn't the hundreds place supposed to be base 4?

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 6:09 pm UTC
by FourTael
Yes, which means it will increase to 1000 after 321. Also, please count along when you reply. Yours was 301 (19).

Mine is 310 (20)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 6:52 pm UTC
by coolguy5678
311 (21)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 6:56 pm UTC
by FourTael
320 (22)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 8:49 pm UTC
by LucasBrown
321 (23)

Re: Count up in a somewhat complex way

Posted: Thu Jan 06, 2011 9:16 pm UTC
by FourTael
1000 (24, aka 4!)

Re: Count up in a somewhat complex way

Posted: Fri Jan 07, 2011 1:00 am UTC
by LucasBrown
1001! (2510)

Re: Count up in a somewhat complex way

Posted: Fri Jan 07, 2011 1:13 am UTC
by FourTael
1010 (26)

Re: Count up in a somewhat complex way

Posted: Wed Jan 12, 2011 6:13 am UTC
by pizzazz
1011 (27)

As an aside, do we know if it is possible to produce all integers this way?

Re: Count up in a somewhat complex way

Posted: Wed Jan 12, 2011 6:51 am UTC
by FourTael
1020 (28)

Absolutely. I actually designed a similar counting system as a kind of code. It can work off any set of numbers agreed upon beforehand. IE pi * sqrt(14) to the eighth decimal place (or to as many places as the two calculators will show). If there's a 1, as in the example (11.754763358538997856165619429959), then the base would be greater than 10. In the example, it would be 11 (because 1 * 10 + next digit, which is 1).

Re: Count up in a somewhat complex way

Posted: Mon Jan 17, 2011 9:01 pm UTC
by Sean Quixote
Uhm, somebody is wrong here - either one of me or all of you :P, yeah, sure makes it seem like it's me, but... From what I understand we're supposed to do, and I'm at least pretty sure that I do, you've all been wrong since the very first post?

Here's the way that I see it:

12 - (110)
102 - (210)
112 - (310)
1002 - (410)
1012 - (510)
1102 - (610)
1112 - (710)
10002 - (810)
10012 - (910)
1013 - (1010)
1023 - (1110)
1103 - (1210)
1113 - (1310)
1123 - (1410)
1203 - (1510)
1213 - (1610)
1223 - (1710)
2003 - (1810)
2013 - (1910)
2023 - (2010)
2103 - (2110)
2113 - (2210)
2123 - (2310)
2203 - (2410)
2213 - (2510)
2223 - (2610)
10003 - (2710)
10013 - (2810)

10023 - (2910)

Shouldn't it be like this? :?:

Re: Count up in a somewhat complex way

Posted: Mon Jan 17, 2011 10:13 pm UTC
by FourTael
No. Not at all. Your number was 1021 (29). There is no single base for the entire number. It changes by the digit. It's this: 15042312.

My number is 1100 (30).

Re: Count up in a somewhat complex way

Posted: Mon Jan 17, 2011 10:59 pm UTC
by Sean Quixote
Oh. Okay, I might be thinking this is more complicated than it is...

So... Mine is...

1101 (31)

?

Re: Count up in a somewhat complex way

Posted: Mon Jan 17, 2011 11:12 pm UTC
by cjdrum
11023 (32)

Wouldn't it make more sense to base the number system of the base 10 number?

Re: Count up in a somewhat complex way

Posted: Mon Jan 17, 2011 11:47 pm UTC
by Sean Quixote
Either I'm comfused yet again, or yours was supposed to be 1110 (32).

Which would make mine 1111 (33).

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 1:40 am UTC
by FourTael
You got it right, Sean.

CJDrum: It's not a single base for all digits. It's a different base for each digit.

1120 (34)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 1:48 am UTC
by Sean Quixote
1121 (35)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 1:51 am UTC
by FourTael
1200 (36)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 1:55 am UTC
by Sean Quixote
1201 (37)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 4:53 am UTC
by FourTael
1210 (38)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 9:19 pm UTC
by Sean Quixote
1211 (39)

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 10:32 pm UTC
by FourTael
1220

Re: Count up in a somewhat complex way

Posted: Tue Jan 18, 2011 11:34 pm UTC
by Sean Quixote
1221 (41)

Re: Count up in a somewhat complex way

Posted: Wed Jan 19, 2011 2:08 am UTC
by FourTael
1300 (42)

Re: Count up in a somewhat complex way

Posted: Wed Jan 19, 2011 2:54 pm UTC
by Sean Quixote
1301 (43)

Re: Count up in a somewhat complex way

Posted: Wed Jan 19, 2011 10:59 pm UTC
by FourTael
1310

Re: Count up in a somewhat complex way

Posted: Thu Jan 20, 2011 3:08 am UTC
by Sean Quixote
1311 (45)

Re: Count up in a somewhat complex way

Posted: Thu Jan 20, 2011 4:01 am UTC
by FourTael
1320 (46)

Re: Count up in a somewhat complex way

Posted: Thu Jan 20, 2011 5:02 am UTC
by Sean Quixote
1321 (47)

Re: Count up in a somewhat complex way

Posted: Thu Jan 20, 2011 7:59 am UTC
by FourTael
2000 (48)

Re: Count up in a somewhat complex way

Posted: Thu Jan 20, 2011 1:41 pm UTC
by Sean Quixote
2001 (49)