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(3): computer exploration by Larry)
for i=[ 800:899 ]
n=char(string(i));
nr=[n(2:end) n(1)];
for b=11:25
try
if base2dec(nr,b)==i
disp([n ' ' nr ' ' char(string(b))])
end
end
end
end
finds
>> moveDigitChangeBase10
825 258 19
>>
and further:
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
finds
382 238 11
for (c)
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Posted by Charlie
on 2022-04-19 18:57:59 |
re(4): computer exploration -- c and d finally
