Help to Find the smallest natural number with these features:

I understand that I must learn math myself, but this exercise isn't as easy as I thought, so I need a help or any advices how to solve it.

So, we have to find the smallest natural [ http://latex.codecogs.com/gif.latex?...n%20\mathbb{N} ] number with these features:

1) The first digit is 1.

2) If we moved 1 to the end of the number, we would get a three times bigger/greater number.

(Thinking)

Re: Help to Find the smallest natural number with these features:

the first digit is 1,

since 3 times the number ends with 1 the original number should end with 7

also the number is divisible by 3.

so you have to check numbers such that : the f number starts with one, ends with seven and divisable by 3

Re: Help to Find the smallest natural number with these features:

Also,

the second digit can not be 9,8,7,6,5

Re: Help to Find the smallest natural number with these features:

Why the original number should end with 7? :)

Re: Help to Find the smallest natural number with these features:

since when you multiply it by three it should end with 1. If you tried other possibility you would never get 1.

Re: Help to Find the smallest natural number with these features:

I know that number can be divisable by 3 if the sum of number's digits is divisable by 3. I tried to find an answer, but I think that I am doing wrong something. I think that number is really big :/ I checked some four-figure numbers, but all of them were wrong. Hmmm :/

Re: Help to Find the smallest natural number with these features:

So how to solve it? (Worried)

Re: Help to Find the smallest natural number with these features:

Re: Help to Find the smallest natural number with these features:

**WOW! Awesome Soroban! Thank you very much!!! (Happy)**

Re: Help to Find the smallest natural number with these features:

Really nice work, but I think you have first to check it for the 3,4 and 5 digits