*
ascending
*
if its digits are strictly increasing. For example, 189 and 3468 are
*
ascending
*
while 142 and 466 are not. For which
*
ascending
*
3 digit number
$n$
(between 100 and 999) is
$6n$
also
*
ascending
*
?

The answer is 578.

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Lets first talk about the digits of 6n. The units digit of it must be 2,4,6,8, or 0 a first glance(Divisible by 6). But as the numbers are ascending in nature, we can further shortlist the first and the last digit combination as (Dashes represent the digits between):

6 _ 8 ; 1 _ _ 4 ; 1 _ _ 6 ; 1 _ _ 8 ; 2 _ _ 6 ; 2 _ _ 8 ; 3 _ _ 6 ; 3 _ _ 8 ; 4 _ _ 6 ; 4 _ _ 8 and 5 _ _ 8. Now we can easily get all the possible 6n values by finding the possible values and using the Divisibility rule for 6. Eventually we get 3468 as the value of 6n and hence n as 578.