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11 September 2008 @ 06:51 am
 
What is 23*302 if the following is true
0+0=1
0+1=2
0+2=3
0+3=00
0+00=01
0+01=02
0+02=03
0+03=10
0+10=11
1+0=2
1+1=3
1+2=00
1+3=01
1+00=02
1+01=03
1+02=10
1+03=11
0*0=0
0*1=1
0*2=2
0*3=3
0*00=00
1*0=1
1*1=00
1*2=10
1*3=20
1*00=30
2*0=2
2*1=10
2*2=30
2*3=010
2*00=030
3*0=3
3*1=20
3*2=010
3*3=100
3*00=130
and so on...
if you don't like this, just skip it

 
 
Current Mood: deviousdevious
 
 
 
freetrav on September 11th, 2008 02:06 am (UTC)
I make it 032320
zemhitchhiker on September 21st, 2008 10:01 pm (UTC)
hint?
ratlan on September 21st, 2008 11:29 pm (UTC)
Reply
Haven't had time to figure out the answer myself.
freetrav on September 22nd, 2008 12:19 am (UTC)
Hmmm...
My answer may be wrong; when I tried doing it again, I got some results that suggest that ASSOCIATIVITY may not work the same way, i.e., (a+b)+c may not be the same as a+(b+c)... Of course, that could just be my screwup.

What's interesting is that we don't seem to have an identity (equivalent to normal 0) for +, although we do have one (equivalent to normal 1) for *. However, what's give does suggest that there SHOULD be an identity for +.

ETA 9/24 09:44 EDT:
There doesn't appear to be a zero-equivalent glyph at all; that means that it can't be a pure place-value system, and about the only way to get the answer is going to be working out the tables that were started with the givens.


Edited at 2008-09-24 01:49 pm (UTC)
freetrav on September 25th, 2008 10:24 pm (UTC)
OK, looking at it from another angle - and one which would support the emoticon of 'devious' - I get 30123 as the answer, in a much quicker analysis.

ratlan, I won't give away my spoilers on this unless/until you say it's OK to do so. As near as I can figure, they're very spoily, to the point where just giving them would lead anyone moderately skilled in math right to the answer.
ratlan on December 2nd, 2008 04:27 am (UTC)
Fin
I haven't been very good at keeping up in the past months. Any spoilers would be nice, as I think I may have accidentally posted something which requires more time than I gave it. I would like to know how you got the answer 30123. At this point, I'm pretty much lost. Thank you for solving this riddle.
freetrav on December 2nd, 2008 06:34 am (UTC)
Re: Fin
CLUE 1: My previous note about no zero-equivalent glyph is correct; there isn't one. There is, however, a glyph with a value equal to the numeric base of the calculation - like if we had a single symbol for the value 'ten' in everyday math, instead of having a zero, and using a one in the tens column to represent the value ten.

So, using * for 'ten', we'd have 5+5=*, 2x5=*, and we'd count 1,2,3,4,5,6,7,8,9,*,11,...19,1*,21...

CLUE 2: The riddle, as given, shows us ALL of the glyphs used in the counting system.