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Re^3: Questions: how to exclude substring having Evil meanings

by holli (Monsignor)
on Dec 03, 2009 at 08:01 UTC ( #810771=note: print w/replies, xml ) Need Help??


in reply to Re^2: Questions: how to exclude substring having Evil meanings
in thread Questions: how to exclude substring having Evil meanings

[...] assuming you didn't want the sequence to be a legal domino sequence.
What if it had to be legal sequences?


holli

You can lead your users to water, but alas, you cannot drown them.

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Re^4: Questions: how to exclude substring having Evil meanings
by ikegami (Pope) on Dec 03, 2009 at 18:46 UTC

    Then each domino except the first only counts for one base 7 digit. 166144047 would go from 16:61:44:04 to 16:66:61:14:44:40:04.

    That means that 6 or more decimal digits would then be more efficient than the same amount of dominos.

    10^n >= 7^(n+1) ln(10^n) >= ln(7^(n+1)) n*ln(10) >= (n+1)*ln(7) n*ln(10) >= n*ln(7) + ln(7) n*ln(10) - n*ln(7) >= ln(7) n*( ln(10) - ln(7) ) >= ln(7) n >= ln(7)/( ln(10) - ln(7) ) n >= 5.455696235812878344 n >= 6
    $ perl -e' printf "chars: %2d digits: %13.f %s dominoes: %11.f\n", $_, 10**$_, qw( < = > )[( 10**$_ <=> 7**($_+1) )+1], 7**($_+1), for 1..12 ' chars: 1 digits: 10 < dominoes: 49 chars: 2 digits: 100 < dominoes: 343 chars: 3 digits: 1000 < dominoes: 2401 chars: 4 digits: 10000 < dominoes: 16807 chars: 5 digits: 100000 < dominoes: 117649 chars: 6 digits: 1000000 > dominoes: 823543 chars: 7 digits: 10000000 > dominoes: 5764801 chars: 8 digits: 100000000 > dominoes: 40353607 chars: 9 digits: 1000000000 > dominoes: 282475249 chars: 10 digits: 10000000000 > dominoes: 1977326743 chars: 11 digits: 100000000000 > dominoes: 13841287201 chars: 12 digits: 1000000000000 > dominoes: 96889010407

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