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Saturday, November 12, 2011

Numbers divisible by seven

Sometimes, doing an exercise runs out of control, slurps time and leads to posts like this:

\begin{array}{l}
111111101101010101001001 \\
111111101101001001010101 \\
111111010101101101001001 \\
111111010101001001101101 \\
111111001001101101010101 \\
111111001001010101101101 \\
101101111111010101001001 \\
101101111111001001010101 \\
101101010101111111001001 \\
101101010101001001111111 \\
101101001001111111010101 \\
101101001001010101111111 \\
10101111111101101001001 \\
10101111111001001101101 \\
10101101101111111001001 \\
10101101101001001111111 \\
10101001001111111101101 \\
10101001001101101111111 \\
1001111111101101010101 \\
1001111111010101101101 \\
1001101101111111010101 \\
1001101101010101111111 \\
1001010101111111101101 \\
1001010101101101111111
\end{array}

you might assume they are binary numbers. They might be, but they are just ordinary decimal numbers consisting of only ones and zeros. They are all divisible by seven. For your convenience I'll show them again, divided by seven this time.

\begin{array}{l}
15873014443001443000143 \\
15873014443000143001443 \\
15873001443014443000143 \\
15873001443000143014443 \\
15873000143014443001443 \\
15873000143001443014443 \\
14443015873001443000143 \\
14443015873000143001443 \\
14443001443015873000143 \\
14443001443000143015873 \\
14443000143015873001443 \\
14443000143001443015873 \\
1443015873014443000143 \\
1443015873000143014443 \\
1443014443015873000143 \\
1443014443000143015873 \\
1443000143015873014443 \\
1443000143014443015873 \\
143015873014443001443 \\
143015873001443014443 \\
143014443015873001443 \\
143014443001443015873 \\
143001443015873014443 \\
143001443014443015873
\end{array}

Even mathematics tries to steal your time, sometimes.
Posted by at 10:30:00 PM
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2 comments:

  1. Gaurav TiwariSunday, November 13, 2011 at 4:33:00 AM GMT+1

    That's hillarious, Sir. Testing divisibility by 7 is extremely tough process.

    ReplyDelete
  2. nilo de roockSunday, November 13, 2011 at 12:19:00 PM GMT+1

    I promise i'll write a note / post about it that shows the trick behind it. I think you will like it, as it involves a lot of symmetry. - Do you the symmetry in the numbers above ?

    ReplyDelete

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