Find the smallest positive base 10 integer, for each of (a) through (d), (but with a 3-digit minimum), such that moving a digit is equivalent to changing the base from 10 to some other base which you must determine, according to one specific condition below:
(a) Moving a 6 from last digit to first changes from base 10 to a smaller base
(b) Moving a 3 from first digit to last changes from base 10 to a smaller base
(c) Moving a 2 from last digit to first changes from base 10 to a larger base
(d) Moving an 8 from first digit to last changes from base 10 to a larger base
Note: The new base may be different for each of (a) to (d)
(In reply to
re(5): computer exploration -- c and d finally by Larry)
Ah, not a typo but a bug:
The two incompatible statements are highlighted:
for i=[ 200:299 2000:2999]
n=flip(char(string(i)));
nr=[n( end) n(1:end-1)];
for b=11:36
if base2dec(nr,b)==i
disp([n ' ' nr ' ' char(string(b))])
end
end
end
The value of n is flipped left-to-right from i, so that i could be in ranges without step values, but the comparison is against the unflipped original. The correct code
for i=[ 200:299 2000:2999]
n=flip(char(string(i)));
nr=[n( end) n(1:end-1)];
for b=11:36
if base2dec(nr,b)==str2double(n)
disp([n ' ' nr ' ' char(string(b))])
end
end
end
compares against the one from which the moved 2 came.
It now, finally(I hope), finds
782 278 18
882 288 19
5272 2527 13
the first of which is that 782 in decimal, translated to base 18 is written as 278.
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Posted by Charlie
on 2022-04-20 14:46:17 |
re(6): computer exploration -- c and d finally
