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Logic Level 3

We say a number is 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 n (between 100 and 999) is 6 n 6n also ascending ?


The answer is 578.

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3 solutions

S.Shri Hari
Jul 12, 2015

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.

Abdeslem Smahi
Jul 12, 2015

i try the number in the problem and hurray 6 n = 3468 6n=3468 lucky ^^

Aditya Chauhan
Jul 12, 2015

I am really excited to see the solution. I just started with some rough calculations and reached 578 × 6 578 \times 6 = 3468

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