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Mirror, Mirror on the wall (Posted on 2004-07-15) Difficulty: 3 of 5
Find the lowest positive integer that has its digits reversed after dividing it by 2.

See The Solution Submitted by SilverKnight    
Rating: 2.0000 (2 votes)

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Solution re: Solution | Comment 7 of 9 |
(In reply to Solution by Tristan)

If all bases are allowed then in base 5, 31/2 = 13, which in decimal comes out to 16/2 = 8.

The results of a computer program that checked numbers up to the previously found 64(decimal) found:

base 5 ; 31 13; decimal  16  8
base 8 ; 52 25; decimal  42  21
base 3 ; 2101 1012; decimal  64  32

The program:

CLS
digits$ = "0123456789abcdefghijklmnopqrstuvwxyz"
FOR n = 1 TO 32
  b = 2
  DO
    n$ = "": n2$ = "": n2 = 0
    t = n
    DO
      d = t MOD b
      t = t \ b
      dig$ = MID$(digits$, d + 1, 1)
      n$ = dig$ + n$
      n2$ = n2$ + dig$
      n2 = n2 * b + d
    LOOP UNTIL t = 0
    IF n2 = 2 * n THEN
      PRINT "base"; b; "; "; n2$; " "; n$; "; decimal "; n2; n
    END IF
    b = b + 1
  LOOP UNTIL LEN(n$) = 1
NEXT

 


  Posted by Charlie on 2004-07-15 23:06:27
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