T is positive integer w/ digits of 0 and 1 only....

[Nekkamath]

Let T be a positive integer whose only digits are Os and 1s. If X=T/12, and x is an integer, what is the smallest possible value of x?

x=101,1001,1010,10101... And none of these are divisible by 12 evenly.

 

[pka]

Re: T as a positive integer

Let T be a positive integer whose only digits are Os and 1s. If X=T/12, and x is an integer, what is the smallest possible value of x?

Do you know the divisibility rules?
If an integer is divisible by 12, then it is divisible by 3 & 4.
Therefore the sum of its digits is a multiple of 3.
Its last two digits must be a multiple of 4.
Does 11100 work?

 

[Nekkamath]

Re: T as a positive integer

Yes, that works. Thank.