Shifting the numbers, part 2

Logic Level 5

$\frac{\overline{ABCDEF}}{\overline{CDEFAB}}=\frac{n}{n+5}$

What is the sum of all positive integers $n <100$ such that there exist a solution for the 6-digit number $\overline{ABCDEF}$ ?

Example : $n=12$ is possible and you may try a related problem here .

This question is part of the set Shifting the numbers .

1 solution

Francis Kong
Nov 11, 2017

$\overline{ABCDEF}$	$\overline{ABCDEF}/\overline{CDEFAB}$	$n$
$131868$	$\frac{12}{17}$	12
$142857$	$\frac{1}{2}$	5
$162162$	$\frac{3}{4}$	15
$384615$	$\frac{5}{6}$	25
$343629$	$\frac{89}{94}$	89

Total is

$12+5+15+25+89 = \boxed{146}$