# Beauty of Mathematics

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

Brilliant, isn't it?

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

# Problem vs Solutions

Problem
One of the most memorable case studies on Japanese management was the case of the empty soap box, which happened in one of Japan's biggest cosmetics companies. The company received a complaint that a consumer had bought a soap box that was empty. Immediately the thorities isolated the problem to the assembly line, which transported all the packaged boxes of soap to the delivery department. For some reason, one soap box went through the assembly line empty. Management asked its engineers to solve the problem. Post-haste,

Solution A
The engineers worked hard to devise an X-ray machine with high-resolution monitors manned by two people to watch all the soap boxes that passed through the line to make sure they were not empty. No doubt, they worked hard and they worked fast but they spent whoopee amount to do so

Solution B
But when a rank-and-file employee in a small company was posed with the same problem, he did not get into complications of X-rays, etc but instead came out with another solution. He bought a strong industrial electric fan and pointed it at the assembly line. He switched the fan on, and as each soap box passed the fan, it simply blew the empty boxes out of the line.

Moral of the story: "Keep It Short & Simple" !! i.e. always look for simple solutions. Devise the simplest possible solution that solves the problem. So, learn to focus on solutions not on problems

# Interesting Facts of English Counting

Letters 'a', 'b', 'c ' & 'd' do not appear anywhere in the spellings of 1 to 99

Letter 'd' comes for the first time in Hundred

Letters 'a', 'b' & 'c ' do not appear anywhere in the spellings of 1 to 999

Letter 'a' comes for the first time in Thousand

Letters 'b' & 'c' do not appear anywhere in the spellings of 1 to 999,999,999

Letter 'b' comes for the first time in Billion

And

Letter 'c' does not appear anywhere in in the spellings of entire English Counting