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142,857

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chrisn-66
1223858.  Tue Jan 31, 2017 5:49 am Reply with quote

I was fascinated to see the number 142,857 appear on the last QI show aired. It was shown that an interesting feature of this number is the fact that when it is multiplied by 2, 3, 4, 5 & 6, each answer contains the same 6 digits as the original number. However, a more interesting fact that wasn't shown is that if you read each answer starting with the number "1", reading through to the end and then returning to the start of the answer to continue, not only are they the same six digits but they also appear in the same sequence as the original number. This pattern does break down when 142,857 is multiplied by 7 where the answer is 999,999 but then another interesting pattern takes over. If 142,857 is then multiplied by 8, 9, 10, 11, 12 & 13, you will have 6 new answers, each with 7 digits. In each case, if you remove the first digit and then add it to the remaining 6, giving you a new 6 digit number, once again you end up with the exact same 6 digits as the original number, and yet again, when read starting with the "1", going to the end then returning to the
start of the answer to continue, they are in the same sequence : 142857.

 

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