PS. Sorry: A mistake (of course)
Teun A. van Dijk
teun at HUM.UVA.NL
Fri Dec 28 17:07:41 UTC 2001
PS. For those interested in numbers, this is just to let them know that
I made a mistake in my calculations of years like 2002 -- i.e. years or
numbers that can be read forward and backward: of course from 10 to 99
there are only 9 such numbers and not 10, beginning with 11. Stupid
mistake.
Not surprising, of course: already my primary school teacher did not
recommend my going to the type of secondary school that prepared for the
university, because I was no good in arithmetic problems, among other
things.... And I only made it to the university because I was stubborn
and never listen to authorities..., and not because I was good at
arithmetic...
Anyway, for those interested, I post the (I hope this time) correct
calculation below.
Enjoy the last days of 2001 and (for Western Euopeans -- except the
Swiss, English...) your last pesetas, guilders, marks, francs, etc.
Cheers
Teun
------------
DATES AND NUMBERS THAT CAN BE READ FORWARD AND BACKWARD
The number of the coming year 2002 can be read in two directions.
The last time this happened was only 11 years ago: in 1991.
The next time however will be in 110 years: in 2112. And so on, each
110 year, until 2992, and then again a jump of 11 to 3003, and again
each 110 year to 3993, and so on to 9999.
And also backward: in steps of 110 years from 1991, 1881,... to 1001,
but then with a short leap of only 2 back to the previous one: 999. And
back again, this time in short steps of 10: 989, 979..., 898, 888,...
until 101.
So how many of these 'palindromic' years did we have since year 1, until
now, 2001?
Well, trivially 9 from 1 to 9 (if we start counting with 1 and not with
0!), and also 9 from 11 to 99.
Then from 101,111,121...191
202,212,222,..292
etc, until 909....999, which is 9 x 10 times= 90.
The interesting thing is that although the range beween 1001 and 9999 is
much bigger than that between 101 and 999 we find the same number of
such palindromic numbers: 90.
So between year 1 and year 2001 we have 9+9+90=108 until 999, + 10 from
1001 until 1991, so 118 'palindromic' years.
If we add another digit we jump to 900 of such palindromic numbers
between 10001 and 99999; but add another digit and we also have 900
between 100001 and 999999.... Depends on whether the total number of
digits is even or uneven.
In a handy formula: we have 9x10 power (n-1)/2 for numbers/years that
have an uneven number of digits, and 9x10 power (n-2)/2 for those who
have an even number of digits....
... if I am not mistaken.
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