Find the lowest positive integer that has its digits reversed after dividing it by 2.

(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