Guest Posted November 5, 2010 Report Share Posted November 5, 2010 a trit is like a bit, but three states instead. a tryte is 6 trits. your goal is to find the fewest number of trytes such that: a) each tryte doesnt differ by less than 2 trits or more than 3 trits from any other tryte b) as many sums as possible are achieved from 0 to 222222(728) (or if you perfer, from ------(-364) to ++++++(+364)) by the addtion of two tytes c) the average of the trytes is as large as possible. your score will be the total number of unique sums achieved * average. havent tried this my self but it looks fun! (yes i have a very wierd sense of fun.) Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted November 5, 2010 Report Share Posted November 5, 2010 a trit is like a bit, but three states instead. a tryte is 6 trits. This puzzle brought a smile, and I'll share briefly why. Not to reveal my age but close to 50 years ago I heard a talk on ternary logic given by my college advisor. Right off the top, and with a wry smile, he speculated one reason it hadn't caught on was the lack of a socially acceptable name for ternary digit. You deftly avoided that issue. Clarifying question [added in edit]: I've usually seen ternary states [the way devices implement ternary logic] as 1, 0 and -1. . Are you specifying a trit's value to be 2, 1 or 0, and calling something like 010221 a tryte?And giving its decimal value [010221 <=> 106] as if it's a base-3 number? . Quote Link to comment Share on other sites More sharing options...
0 araver Posted November 6, 2010 Report Share Posted November 6, 2010 (edited) And adding to bonanova's 2 questions: 3. If yes to the previous two questions then what do you understand through addition of two trytes? Or equivalently, is the set of trytes closed under this operation e.g. 222222 + 000001 = 000000? (addition modulo 729) Edited November 6, 2010 by araver Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 7, 2010 Report Share Posted November 7, 2010 all good questions: 1) a trit can be 0,1,2 or -1,0,1 (-,0,+) either way is fine, as long as you are consistent. 2) correct. 3) i had originally meant the puzzle for regular base 10 addition, but i like yours better, let's go with that.\ Quote Link to comment Share on other sites More sharing options...
0 araver Posted November 7, 2010 Report Share Posted November 7, 2010 is 13195.(63) Obtained by 11 trytes: 222220 222212 222201 222122 222021 221222 220221 212222 202221 122222 022221 Average: 628.(36) Unique sums: 21 Quote Link to comment Share on other sites More sharing options...
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Guest
a trit is like a bit, but three states instead.
a tryte is 6 trits.
your goal is to find the fewest number of trytes such that:
a) each tryte doesnt differ by less than 2 trits or more than 3 trits from any other tryte
b) as many sums as possible are achieved from 0 to 222222(728) (or if you perfer, from ------(-364) to ++++++(+364)) by the addtion of two tytes
c) the average of the trytes is as large as possible.
your score will be the total number of unique sums achieved * average.
havent tried this my self but it looks fun! (yes i have a very wierd sense of fun.)
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