Friday, June 19, 2009

Digit Juggles that make you Giggle

Some of the strange revelations I have had and verified with my Mathematics Mentor, PI(who is PI? When the right time comes, I will let all know...!) are as follows:

  • 1089 x 9 = 9801. It is just the reverse of 1089.
  • 142857 - A Cyclic Number.
142857 × 1 = 142857
142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285
142857 × 6 = 857142

Being a 7 digit number, on multiplying by 7, it gives out an awesome number.
142857 × 7 = 999999

And now it gets strange, one of the digit splits.
142857 × 8 = 1142856------------7 got split into 1 & 6
142857 × 9 = 1285713------------4 got split into 1 & 3
142857 × 10 = nothing interesting
142857 × 11 = 1571427-----------8 got split into 1 & 7
142857 × 12 = 1714284-----------5 got split into 1 & 4
142857 × 13 = 1857141-----------2 got split into 1 & 1

Once again strange output. Well even at 7 it does the same weird output.
142857 × 14 = 1999998

For other multiples, please help yourself.

Another interesting fact about this number is it is omnipresent. Divide any number that is not a multiple of 7 or 10 and you always see it in the decimal part in recurring form. Don't believe me, try it.
By the way, I got this from my acquaintance, Piyu

  • Another one like 1089. 21978 x 4 = 87921
  • Forty, is the only number which has the letters arranged in alphabetical order
  • Square 13 = 169. Reverse it = 961, it is the square of 31
  • (1 x 9) + 2 = 11. (12 x 9) + 3 = 111. (123 x 9) + 4 = 1111. (1234 x 9) + 5 = 11111 and so on and so forth
  • 111,111,111 x 111,111,111 = 12,345,678,987,654,321. Funny isn't it?
  • 7641 - 1467 = 6174