# 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?

Result

x =  1

#### Solution:

$n = 962 \ \\ n_{ 1 } = n/4 = 962/4 = \dfrac{ 481 }{ 2 } = 240.5 \ \\ n_{ 2 } = \lfloor n_{ 1 } \rfloor = \lfloor 240.5 \rfloor = 240 \ \\ n_{ 3 } = n-4 \cdot \ n_{ 2 } = 962-4 \cdot \ 240 = 2 \ \\ \ \\ s = n_{ 2 } \cdot \ (1+2+3+4) + 1 + 2 = 240 \cdot \ (1+2+3+4) + 1 + 2 = 2403 \ \\ s_{ 3 } = s/3 = 2403/3 = 801 \ \\ \ \\ 1234 1234 ... 1234 12 \ \\ x = 1$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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