Magical Numbers
"The numbers when Multiplied/Added/Subtracted/Divided by some other numbers gives amazing results are ‘Magical Numbers’".
Examples:
( 1) Magic in multiplication of 37 with multiple of 3.
37 × 3 = 111
37 × 6 = 222
37 × 9 = 333
37 × 12 = 444
37 × 15 = 555
( 2) The beauty of mates.
(1 × 9) + 2 = 11
(12 × 9) + 3 = 111
(123 × 9) + 4 = 1111
(1234 × 9) + 5 = 11,111
( 3) Magic in multiplication of 3367 with multiple of 3.
3367 × 3 = 10,101
3367 × 6 = 20,202
3367 × 9 = 30,303
3367 × 12 = 40,404
( 4) Magic in multiplication of 15873 with multiple of 7.
15873 × 7 = 111, 111
15873 × 14 = 222, 222
15873 × 21 = 333, 333
15873 × 28 = 444, 444
( 5) Magical numbers in the square of 333….4.
34 × 34 = 1156
334 × 334 = 111, 556
3334 × 3334 =111, 155, 56
( 6) Multiplication of 11111… with its self.
11 × 11 =121
111 × 111 = 12,321
1111 × 1111 =1,234,321
( 7) Magical numbers 3 , 6 , 9 , 12 , …
3 = 3(2)/2
3 + 6 = 6(3)/2
3 + 6 + 9 = 9(4)/2
3 + 6 + 9 + 12 = 12(5)/2
( 8) Magical number 2….
2 = 4 - 2
2 + 4 = 8 - 2
2 + 4 + 8 = 16 - 2
2 + 4 + 8 + 16 = 32 – 2
( 9) Magical numbers 5 & 6….
5(6) = 6 (6 -1)
5(6) + 5(36) = 6 (36 - 1)
5(6) + 5(36) + 5(216) = 6 (216 - 1)
5(6) + 5(36) + 5(216) + 5(1296) = 6 (1296 - 1)
( 10) Look at the last function in the denominator on the left-hand side.
1 / 2 × 1 = 1 / 2
1 / 2 × 1 + 1 / 2 × 3 = 2 / 3
1 / 2 × 1 + 1 / 2 × 3 + 1/3 × 4 = 3 / 4
1 / 2 × 1 + 1 / 2 × 3 + 1/3 × 4 + 1/4×5 = 4 / 5
( 11) Sum of ‘ n ’ odd natural numbers is always ‘ n2 ’
1 = 12
1 + 3 = 22
1 + 3 + 5 = 32
1 + 3 + 5 + 7 = 42
1 + 3 + 5 + 7 + 9 = 52
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