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 Mirror, Mirror on the wall (Posted on 2004-07-15)
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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 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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