### Curious 56

Curious 56's:

(111+1)/(1+1) = 56

(222+2)/(2+2) = 56

(333+3)/(3+3) = 56

...

(999+9)/(9+9) = 56

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Curious 56's:

(111+1)/(1+1) = 56

(222+2)/(2+2) = 56

(333+3)/(3+3) = 56

...

(999+9)/(9+9) = 56

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A unique value of pi.

x = (pi + 3)/2

2x =pi + 3

2x(pi - 3) = (pi + 3)(pi - 3)

2(pi)x - 6x = pi^2 - 9

9 - 6x = pi^2 - 2(pi)x

9 - 6x + x^2 = pi^2 - 2(pi)x + x^2

(3 - x)^2 = (pi - x)^2

3 - x =pi - x

3 = pi

But pi does not equal 3!

What is wrong here?

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Curious multiplications using 1's:

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

etc...

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Benford's law, also called the first-digit law, first digit phenomenon, or leading digit phenomenon, states that in lists of numbers from many real-life sources of data, the digit 1 occurs almost one-third of the time, much greater than the expected 11.1% (i.e., one digit out of 9). The increasingly larger numbers occur less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty.

This counter-intuitive result applies to a wide variety of figures, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants. It is named after physicist Frank Benford, who stated it in 1938. It had been previously stated by Simon Newcomb in 1881. The first rigorous formulation and proof was made by Theodore Hill in 1988.

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Curious arrangements with 9's:

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1 111

1234 x 9 + 5 = 11 111

12345 x 9 + 6 = 111 111

123456 x 9 + 7 = 1 111 111

1234567 x 9 + 8 = 11 111 111

12345678 x 9 + 9 = 111 111 111

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