Monday, March 17, 2014

MATHEMATICA 9 SAGITTARIUS


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Pick a number between one and 10.

Multiply it by nine.

Add the two digits of the resulting number together.

Now subtract five from that.

Take your number and match it up with a letter of the alphabet (so 1 would be A, 2 would be B, etc.).

Pick a country that begins with that letter.

Pick an animal whose name begins with the last letter of the country name.

Pick a fruit that begins with the last letter of the animal's name.

Denmark, kangaroo and orange

From Wikipedia: 9

In base 10 a positive number is divisible by nine if and only if its digital root is 9.[9] That is, if you multiply nine by any natural number, and repeatedly add the digits of the answer until it is just one digit, you will end up with nine: 
2 × 9 = 18 (1 + 8 = 9)
3 × 9 = 27 (2 + 7 = 9)
9 × 9 = 81 (8 + 1 = 9)
121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 9)
234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)
578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27; 2 + 7 = 9)
482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45; 4 + 5 = 9) 
There are other interesting patterns involving multiples of nine: 
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 81 = 999999999 
The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Examples: 
The sum of the digits of 41 is 5, and 41-5 = 36. The digital root of 36 is 3+6 = 9, which, as explained above, demonstrates that it is divisible by nine. 
The sum of the digits of 35967930 is 3+5+9+6+7+9+3+0 = 42, and 35967930-42 = 35967888. The digital root of 35967888 is 3+5+9+6+7+8+8+8 = 54, 5+4 = 9. 
Subtracting two base-10 positive integers that are transpositions of each other yields a number that is a whole multiple of nine. Examples: 
41 - 14 = 27 (2 + 7 = 9)
36957930 - 35967930 = 990000, a multiple of nine. 
This works regardless of the number of digits that are transposed. For example, the largest transposition of 35967930 is 99765330 (all digits in descending order) and its smallest transposition is 03356799 (all digits in ascending order); subtracting pairs of these numbers produces: 
99765330 - 35967930 = 63797400; 6+3+7+9+7+4+0+0 = 36; 3+6 = 9.
99765330 - 03356799 = 96408531; 9+6+4+0+8+5+3+1 = 36; 3+6 = 9.
35967930 - 03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18; 1+8 = 9. 
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers, known as long ago as the 12th Century 
If you divide a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal. (e.g. 274/999 = 0.274274274274...)



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