Page **1** of **64**

### 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_{!} (25_{10})

### 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

, 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:

1

_{2} - (1

_{10})

10

_{2} - (2

_{10})

11

_{2} - (3

_{10})

100

_{2} - (4

_{10})

101

_{2} - (5

_{10})

110

_{2} - (6

_{10})

111

_{2} - (7

_{10})

1000

_{2} - (8

_{10})

1001

_{2} - (9

_{10})

101

_{3} - (10

_{10})

102

_{3} - (11

_{10})

110

_{3} - (12

_{10})

111

_{3} - (13

_{10})

112

_{3} - (14

_{10})

120

_{3} - (15

_{10})

121

_{3} - (16

_{10})

122

_{3} - (17

_{10})

200

_{3} - (18

_{10})

201

_{3} - (19

_{10})

202

_{3} - (20

_{10})

210

_{3} - (21

_{10})

211

_{3} - (22

_{10})

212

_{3} - (23

_{10})

220

_{3} - (24

_{10})

221

_{3} - (25

_{10})

222

_{3} - (26

_{10})

1000

_{3} - (27

_{10})

1001

_{3} - (28

_{10})

1002

_{3} - (29

_{10})

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: 1_{5}0_{4}2_{3}1_{2}.

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**

1102_{3} (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)