Palindromic Year MMII

World!Of Numbers		HOME plate WON \|
Facts and figures about 2002 the last palindromic year... that most of us will live to see! part 2
year2002 part 1

We live in 2002 and 878 years from now...
Are these two palindromes predicting a catastrophy !

Will asteroid 1950DA hit the earth in 2880 ?
Note that 2880 = 2002 + 878, the sum of our two palindromes !

Read Amir Alexander's article from April 12, 2002

A Close Call for Earth in 878 Years

The above link was sent to me by G. L. Honaker [email][site] (dd. 21/04/2002),
a loyal submitter to my website! Thanks.

(pdg) Not so long ago I saw a movie Armageddon where a bunch
of oildiggers fixed another orbital bug. So I am confident for
the future. Palindromes (and humanity I hope) will survive 2880.

Chocolate Mathematics

Enoch Haga [email] forwarded me some fun maths (dd. 23/04/2002) -

" THIS IS THE ONLY YEAR (2002) IT WILL EVER WORK,

SO SPREAD IT AROUND WHILE IT LASTS. "

This is pretty neat how it works out.
This is cool chocolate math !!!!!!
  DON'T CHEAT BY SCROLLING DOWN FIRST!
   It takes less than a minute...
    Work this out as you read.
     Be sure you don't read the bottom until
      you've worked it out! This is not
       one of those waste of time things, it's fun.

First of all, pick the number of times a week that you would like
to have chocolate (try for more than once but less than 10).

Multiply this number by 2 (just to be bold).

Add 5 (for Sunday).

Multiply it by 50. I'll wait while you get the calculator...

If you have already had your birthday this year add 1752 ...
If you haven't, add 1751 ...

Now subtract the four digit year that you were born.

You should have a threedigit number...
The first digit of this was your original number
(i.e., how many times you want to have chocolate each week).
The next two numbers are...

A 13 x 13 Magic Square with Magic Sum 2002...
(by Kishor N. Gordhandas from Bombay, India). (email dd. 8/10/2002)

The 169 cells of this super Magic Square are filled with all the integers
continuously from 70 up to 238.

188	190	122	116	111	199	196	110	73	229	78	234	156
120	118	186	192	197	109	112	198	235	79	230	152	74
115	121	191	189	114	200	195	107	238	71	153	77	231
193	187	117	119	194	108	113	201	70	155	237	232	76
131	177	175	133	97	81	227	211	154	236	72	75	233
136	172	185	123	221	218	150	93	88	146	162	149	159
138	170	124	184	157	89	84	228	212	164	144	165	143
206	102	176	132	80	224	219	151	96	161	147	160	148
210	98	104	204	215	158	90	87	220	145	163	142	166
106	202	140	134	103	127	209	183	182	83	225	217	91
179	129	174	168	205	181	99	125	126	95	213	223	85
139	167	137	173	203	101	128	208	130	222	86	94	214
141	169	171	135	105	207	180	100	178	216	92	82	226

Some interesting peculiarities

This 13 x 13 = 169 Magic Square has a special number, namely 154 , which I call
the Magic Number. This number is common to many other smaller Magic Squares
inside this Super Magic Square.

There are the following smaller squares that you will find inside.
Four 4 x 4 = 16 squares with Magic Sum = (154 x 4) = 616 (top_left marked green)
Two 5 x 5 = 25 squares with Magic Sum = (154 x 5) = 770 (top_left = 73 & 97)
Two 7 x 7 = 49 squares with Magic Sum = (154 x 7) = 1078 (top_left = 114 & 175)
Two 9 x 9 = 81 squares with Magic Sum = (154 x 9) = 1386 (top_left = 111 & 131)
One 11 x 11 = 121 square with Magic Sum = (154 x 11) = 1694 (top_left = 115)
One main 13 x 13 = 169 square with Magic Sum = (154 x 13) = 2002
This is possible because 2002 = 2 x 7 x 11 x 13.

The top_left corners of the four 4 x 4 = 16 Magic Squares
with palindromic ! Magic Sum 616 are marked with a green background.

You will be able to find the other Magic sub_Squares quite easily.
ps. there exist one 3 x 3 = 9 square that is not perfect pandiagonal
since one of the diagonals sums to 465 instead of the Magic Sum 462.
154 marks the bottom_left corner of this square.

The main square has been drawn and inner squares have been
colourmarked wherever possible resulting in the file 'Magic 2002.jpg'.
All this was prepared for me by the use of the computer of my
artist friend. I hope everything is OK. This jpg file of 119 KB
is available by simple email request.

No doubt you will like and enjoy the square.

A General Year 2002 Arithmetic Puzzle
(by Bruce A. Berentsen, Ph. D., Mathematician & Software Developer).
(email dd. 26/10/2002)

Using integers 1 through 9 exactly once, and using either operators
+ or * between adjacent integers, develop an expression that yields
the value 2002.

a. Integers 1 through 9 are to be used exactly once, in any order.
b. Parentheses are permitted.
c. Integers used in the expression are not allowed to be a
concatenation of digits.
d. Only operators + and * are permitted between adjacent integers.

Bruce's puzzle is a variation to a NPR Current Challenge given out
dd. October 6, 2002 by Erich Friedman.

Write out the digits from 1-9 in order. Then add some plus (+) signs
and times (x) signs to the string to make it add up to 2,002. As usual
in arithmetic, multiplication is done before addition, and you don't
have to put a sign between every 2 digits.
Answers

1 x 2 + 34 x 56 + 7 + 89 = 2002
and

1 x 23 + 45 x 6 x 7 + 89 = 2002

Solution
Bruce came out with the following two distinct solutions
without the use of a computer [ October 29, 2002 ].

1 * 2 * ( 5 + 6 ) * ( 3 * 4 + 7 + 8 * 9 ) = 2002 (courtesy of Bob Haymond)
and

(((( 9 + 7 ) * 5 + 3 ) * 4 * 6 ) + 2 + 8 ) * 1 = 2002 (by Bruce himself)

A computer program would have to be written to enumerate all possible solutions.
Who's candidate ?

Terry Trotter (email dd. 04/01/2003)
writes that this digital topic is one of his favorites.
(it's like my All the King's Digits project "make a 100" in Math Forum.)
"Could 0 be included there, at least in the large-to-small order ?" he wonders...

December 2002 is quite a month
(by Norma Smith, Universal Harmonics,
Master Analyst and Timekeeper). (email dd. 5/12/2002)

December = 55 (alpha)numerically, and is a Master Number or iterated
number such as 11, 22, 33, 99 and 111, 333, 888, 999. These calendar dates
are the numerical sum of a month + the date ( A=1, B=2, Z=26 ).
E.g. D-E-C-E-M-B-E-R = 4+5+3+5+13+2+5+18 = 55.

Months that have dates adding up to a Master Number of double digits
are 11 days apart... 11 + 11 = 22, + 11 = 33, etc. Notice this 11 theme
in the following data.

The 11 day Master Number cycles begin with December 1 to December 11^th.
Thus, 55 + 11 = 66 as December 11. Eleven days later is 77, on Dec 22
( December as 55 + 22^nd = 77 ).

Interesting that 23^rd as 23 = End. It is the end of Master Number
cycles for this month and this year.

December 2002 is also the end of the unique 11 year Time Window from
1991 to 2002. These Mirror Years / Palindrome Years occur each century
110 years apart, thus the break in the 110 year cycle is unique.

I can verify the book end, flip-flop, opposites or polarity effect in
my life these past 11 years: major change has occured since I first
noticed the 1991 numerical oddity.

There is so much (esoteric!) interpretation that comes to the mind...

More facts and figures of the palindrome 55 at WONplate 81

2002 at a palindromic position

in the decimal expansion of

.
(PDG dd. 16/12/2002)

The string 2002 was found at palindromic position 8622268 counting

from the first digit after the decimal point. The 3. is not counted.

Immediately we see that all the digits are even (2002 as 8622268).
The factorization of 8622268 = 2 * 2 * 373 * 5779 contains
another palindrome ! Note that 5779 - 2 - 2 = 5775 yet another palindrome !

Try to find the first palindromic positions in Pi for the following numbers :
or add entries yourself for whatever interesting reason...

313

858 (equal length!), 632236

373

24242 (smoothly undulating!)

1991

2002

8622268 (all digits even)

2003

2112

8622268

Find the first PRIME (+palindromic?) positions in Pi for the following numbers :

373

1991

2002

2003

2112

8622268

What is the longest known string (and at what position) found in Pi
that contains only EVEN or only ODD digits, or with digits that
continually changes parities ?

un an � nu - A 2002 compilation.
(by Jean Louis Quirighetti (email)) dd. July 9, 2003

Jean Louis likes to give to everyone, with a little delay, his best
wishes for 2002 ! He only very recently discovered this webpage.

This compilation (available in pdf format) encompasses many
palindromic and above all artistic themes from a variety of fields.
I'd like to highlight the one with numerical content :

2002 = 1 + 666 + 1 + 666 + 1 + 666 + 1 =
1 + (1x1x1) +�(2x2x2) +�(3x3x3) +�(4x4x4) +�(5x5x5) +�(6x6x6) +
(5x5x5) +�(4x4x4) +�(3x3x3) +�(2x2x2) +�(1x1x1) +�1 + (1x1x1) +
(2x2x2) +�(3x3x3) +�(4x4x4) +�(5x5x5) +�(6x6x6) +�(5x5x5) +�(4x4x4) +
(3x3x3) +�(2x2x2) +�(1x1x1) + 1 + (1x1x1) +�(2x2x2) +�(3x3x3) +�(4x4x4) +
(5x5x5) +�(6x6x6) +�(5x5x5) +�(4x4x4) +�(3x3x3) +�(2x2x2) +�(1x1x1) +�1

666's palindromic decomposition by G. Hainry - www.univ-lemans.fr
(Source : 37 et le palindrome du Diable)

By simple email request one can obtain this [2002, un an � nu.pdf] file format
compilation. Its size is 1028 KB and contains 25 beautiful 'layout' pages.

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