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Alphanumber

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Alphanumber is a numeric code for a letter or a word. The alphanumbers for letters A–Z is 1–26. After Z, the letter would be AA through AZ, BA through BZ all the way through ZZ. After ZZ, it would be AAA and go all the way through ZZZ, and so on. The number for letters that contains only the number of Zs can be determined by the following formula:

26^{Z} + 26^{Z-1}

where Z is the number of Zs.

The number for ZZ would be 702 since it is 262 + 262−1. The number for ZZZ would be 18278 since 263 + 263−1.

To convert the words into alphanumbers, here's the formula below:

(\alpha \times 26^0) + (\alpha \times 26^1) + (\alpha^2 \times 26^2) + (\alpha \times 26^3)\ldots up till the power number of 26 is determined by number of letters in a word −1

where \alpha is the alphanumber of letter.

For example, my favorite word is girl. Here's the equation below to calculate the alphanumber of girl:

(l × 260) + (r × 261) + (i × 262) + (g × 263).

Notice the letters spell backwards going left to right in the equation, that's what we have to do. Now lets continue:

(12 × 260) + (18 × 261) + (9 × 262) + (7 × 263)
(12 × 1) + (18 × 26) + (9 × 676) + (7 × 17576)
12 + 468 + 6084 + 123032 = 129596.

So the alphanumber of girl is 129596.

Lets do another equation. Lets do ABC:

(3 × 260) + (2 × 261) + (1 × 262)
(3 × 1) + (2 × 26) + (1 × 676)
3 + 52 + 676 = 731.

So the alphanumber of ABC is 731.

So lets teach you how to convert alphanumbers into comboletters:

n - (p/26^2)\downarrow26^2 - (p/26^1)\downarrow26^1 - (p/26^0)\downarrow26^0

where

n is the starting number
p is the previous number.
\downarrow is to round down the number.

Lets incorporate the current year 2011 into the formula:

2011 − (2011/262)↓262 = 659 − (659/261)↓261 = 9
2011 − 2.97↓262 = 659 − 25.35↓261 = 9
2011 − 2(262) = 659 − 25(261) = 9
2011 − 2(676) = 659 − 25(26) = 9
2011 − 1352 = 659 − 650 = 9.

So the factor numbers 2, 25, 9 infront of parentheses in evaluations 3 & 4 become B, Y, I and combine it together we get BYI. So the numeric comboletter of 2011 is BYI.

So lets convert alphanumber into a secret word. Lets do 347508. So we start with 263 which is 17576 but we can't start with 264 which is 456976, which is greater than 347508:

347508 − (347508/263)↓263 = 13564 − (13564/262)↓262 = 44 − (44/261)↓261 = 18
347508 − 19.77↓263 = 13564 − 20.07↓262 = 44 − 1.69↓261 = 18
347508 − 19(263) = 13564 − 20(262) = 44− 1(261) = 18
347508 − 19(17576) = 13564 − 20(676) = 44 − 1(26) = 18
347508 − 333944 = 13564 − 13520 = 44 − 26 = 18.

So the factors 19, 20, 1, 18 infront of parentheses in evaluations 3 & 4 become S, T, A, R and combine it into STAR. So the numeric word of 347508 is star.

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