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Move the digit, Change the base (Posted on 2022-04-19) Difficulty: 3 of 5
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)

No Solution Yet Submitted by Larry    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Summary -- if it had been right from the start Comment 10 of 10 |
(a)

for i=[106:10:9996  ]
  n= char(string(i));
  nr=[n( end) n(1:end-1)];
  for b=9:-1:7
    try
    if base2dec(nr,b)==i
      disp([n ' ' nr ' ' char(string(b))])
    end
    end
  end
end

finds

dec b-n  n
316 631 7

(b)

for i=[300:399 3000:3999  30000:39999  300000:399999]
  n= (char(string(i)));
  nr=[ n(2:end), n(1)];
  for b=9:-1:4
    try
    if base2dec(nr,b)==i
      disp([n ' ' nr ' ' char(string(b))])
    end
    end    
  end
end

>> moveDigitChangeBase10
361020 610203 9
>> 

(c)

for i=[102:10:9992  2000:2999]
  n= 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

782 278 18
882 288 19
5272 2527 13

(d)

for i=[800:899 8000:8999  80000:89999  800000:899999]
  n= (char(string(i)));
  nr=[ n(2:end), n(1)];
  for b=11:20
     
    if base2dec(nr,b)==i
      disp([n ' ' nr ' ' char(string(b))])
    end    
    
  end
end

finds

825 258 19
8200 2008 16
853311 533118 11

  Posted by Charlie on 2022-04-21 09:17:31
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