# By six

From the digits 1,2,3,4 we create the long integer number 123412341234. .. .. , which will have 962 digits. Is this number divisible by 6?

Correct result:

x =  1

#### Solution:

$n=962 \ \\ n_{1}=n/4=962/4=\dfrac{ 481 }{ 2 }=240.5 \ \\ n_{2}=\lfloor n_{1} \rfloor=\lfloor 240.5 \rfloor=240 \ \\ n_{3}=n-4 \cdot \ n_{2}=962-4 \cdot \ 240=2 \ \\ \ \\ s=n_{2} \cdot \ (1+2+3+4) + 1 + 2=240 \cdot \ (1+2+3+4) + 1 + 2=2403 \ \\ s_{3}=s/3=2403/3=801 \ \\ \ \\ 1234 1234 ... 1234 12 \ \\ x=1$

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