Count up in a somewhat complex way
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Count up in a somewhat complex way
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
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
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
Re: Count up in a somewhat complex way
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)
121 (11)
Re: Count up in a somewhat complex way
Very well.
200 (12)
200 (12)
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
Re: Count up in a somewhat complex way
Wasn't the hundreds place supposed to be base 4?
Re: Count up in a somewhat complex way
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)
Mine is 310 (20)

 Posts: 16
 Joined: Sat Feb 13, 2010 12:20 pm UTC
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
Re: Count up in a somewhat complex way
1000 (24, aka 4!)
 LucasBrown
 Posts: 299
 Joined: Thu Apr 15, 2010 2:57 am UTC
 Location: Poway, CA
Re: Count up in a somewhat complex way
1010 (26)
Re: Count up in a somewhat complex way
1011 (27)
As an aside, do we know if it is possible to produce all integers this way?
As an aside, do we know if it is possible to produce all integers this way?
Re: Count up in a somewhat complex way
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).
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).
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
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?
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
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).
My number is 1100 (30).
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
Oh. Okay, I might be thinking this is more complicated than it is...
So... Mine is...
1101 (31)
?
So... Mine is...
1101 (31)
?
Re: Count up in a somewhat complex way
1102_{3} (32)
Wouldn't it make more sense to base the number system of the base 10 number?
Wouldn't it make more sense to base the number system of the base 10 number?
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
Either I'm comfused yet again, or yours was supposed to be 1110 (32).
Which would make mine 1111 (33).
Which would make mine 1111 (33).
Re: Count up in a somewhat complex way
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)
CJDrum: It's not a single base for all digits. It's a different base for each digit.
1120 (34)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1121 (35)
Re: Count up in a somewhat complex way
1200 (36)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1201 (37)
Re: Count up in a somewhat complex way
1210 (38)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1211 (39)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1221 (41)
Re: Count up in a somewhat complex way
1300 (42)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1301 (43)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1311 (45)
Re: Count up in a somewhat complex way
1320 (46)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
1321 (47)
Re: Count up in a somewhat complex way
2000 (48)
 Sean Quixote
 Posts: 229
 Joined: Tue Sep 14, 2010 1:20 am UTC
 Location: Ubekibekibekibekistanstan
Re: Count up in a somewhat complex way
2001 (49)
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