Beauty of Maths:

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

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

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

and finally take a look at this symmetry

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

WOW

Nice !

Very tricky math!
(This must be done in your head only. DO NOT use paper and pencil or a calculator. Try it)
Question:::::Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?
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ANSWER:::Did you get 5000? The correct answer is actually 4100.Don't believe it? Check with your calculator! ;)

nicee one chicago bull

i got 4100
whats the problem?

Seems Genius

Bull doesn't know how to add.

Thats Y I asked u guys

Math is good.

Another Question. What is the size of largest square that can be inscribed in a unit cube?
Note** The answer can be easily googled so the important thing is not the answer
itself it is the process. Lets see how many unique processes can we see.

Square formed in diagonal of the cube.

@bluemoon close enough, now can you calculate the size too and post the
method as well.

Even though I don't have an answer, I don't think blue_moon's answer is close enough. I will try to solve it. Good question.

@propensity Good luck!!

divdude,

Let us consider a unit cube lying on a plane on one of its faces. When a vertical plane passing through a diagonal of the cube's horizontal faces is slowly rotated about a line that is parallel to the diagonal but passes through the center of the cube, a time will come when the intersection points of the plane and two pairs of diagonally opposite edges of the cube will exactly form a square. This will be the largest square that can be inscribed in the cube.

If the plane intersects each of these edges at a distance of x from the diagonally opposite vertices of the cube, then for the intersection to be a square,

x^2 + x^2 = (1-x)^2 + (1-x)^2 + 1

which implies x = 3/4.

The length of each side of the square is then (3/4)*(2)^0.5. So the square's area will be 9/8.

@gemmi nice work. Very intuitive method. Fellas any more methods?

Thats the one I was saying

ok i think the beauty part was over after i posted my original stuff....all these are ugliness of maths :P

@lurey lol
As they say beauty is in the eyes of beholder.