Friday, 23 September 2011

Beauty of Mathematics - Magic


Sequential Inputs of numbers with 8
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Sequential 1's with 9
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111


Sequential 8's with 9
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Numeric Palindrome with 1's
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

Without 8
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999

Sequential Inputs of 9
9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001
9999 x 9999 = 99980001
99999 x 99999 = 9999800001
999999 x 999999 = 999998000001
9999999 x 9999999 = 99999980000001
99999999 x 99999999 = 9999999800000001
999999999 x 999999999 = 999999998000000001
......................................

Sequential Inputs of 6
6 x 7 = 42
66 x 67 = 4422
666 x 667 = 444222
6666 x 6667 = 44442222
66666 x 66667 = 4444422222
666666 x 666667 = 444444222222
6666666 x 6666667 = 44444442222222
66666666 x 66666667 = 4444444422222222
666666666 x 666666667 = 444444444222222222
......................................

Roman Numbers :


    Roman numerals were originated in ancient Rome. It is based on certain letters which are given values as numerals.
Roman Numerals are widely used nowadays, in clocks, books, numberlists, etc.,. 
1
I
2
II
3
III
4
IV
5
V
6
VI
7
VII
8
VIII
9
IX
10
X
11
XI
12
XII
13
XIII
14
XIV
15
XV
16
XVI
17
XVII
18
XVIII
19
XIX
20
XX
21
XXI
22
XXII
23
XXIII
24
XXIV
25
XXV
26
XXVI
27
XXVII
28
XXVIII
29
XXIX
30
XXX
31
XXXI
32
XXXII
33
XXXIII
34
XXXIV
35
XXXV
36
XXXVI
37
XXXVII
38
XXXVIII
39
XXXIX
40
XL
41
XLI
42
XLII
43
XLIII
44
XLIV
45
XLV
46
XLVI
47
XLVII
48
XLVIII
49
XLIX
50
L
51
LI
52
LII
53
LIII
54
LIV
55
LV
56
LVI
57
LVII
58
LVIII
59
LIX
60
LX
61
LXI
62
LXII
63
LXIII
64
LXIV
65
LXV
66
LXVI
67
LXVII
68
LXVIII
69
LXIX
70
LXX
71
LXXI
72
LXXII
73
LXXIII
74
LXXIV
75
LXXV
76
LXXVI
77
LXXVII
78
LXXVIII
79
LXXIX
80
LXXX
81
LXXXI
82
LXXXII
83
LXXXIII
84
LXXXIV
85
LXXXV
86
LXXXVI
87
LXXXVII
88
LXXXVIII
89
LXXXIX
90
XC
91
XCI
92
XCII
93
XCIII
94
XCIV
95
XCV
96
XCVI
97
XCVII
98
XCVIII
99
XCIX
100
C

200
CC
300
CCC
400
CD
500
D
600
DC
700
DCC
800
DCCC
900
CM
1000
M

An accurate way to write the roman numbers is to first take the thousands, hundreds, tens and units.
Example:
1999, one thousand is M, nine hundred is CM, ninety is XC, nine is IX. Combine all these:
MCMXCIX