z = X(d^d+L)

S=Z/D is the number line’s length

L=length of string

X=how many strings

d=hamming distance

S / RT = custom choice for 1st farthest string(eg. enter 1) and 2nd farthest string (eg. 2 for 2nd farthest, etc)

The script is simple.

`1 INPUT "LENGTH OF STRING";L 2 INPUT "X FOR HOW MANY";X 3 INPUT "D FOR HAMMING DISTANCE";D 4 Z = X*(d^d+L) 5 S = Z / D 6 INPUT "ENTER # FOR NEXT STRING";RT 7 PRINT"YOUR CLOSEST STRING"RT, S / RT 8 INPUT "WOULD YOU LIKE TO GO BACK FOR MORE STRING?";M 9 IF M=1 THEN GOTO 6 ELSE GOTO 10 10 PRINT"GAME OVER" `

You take the data output if its a whole or near whole number and write it on a paper number line. I have a picture at the end of the question to prevent confusion.

*Rules of Game.*

*Rounds are based on length of string. Round 2 is 2 character strings. Assuming d is fixed or increases*

*Never go over the line’s number limit.*

*(eg. never go over 30!)*

*The game has unlimited rounds and data is recorded written down on a chart of strings that are numerically listed*

*Points gathered up and winner is selected.*

*The objective of the game is to keep playing until its to hard and just quit.*

All strings are alphabetically organized. You try to find all the strings that are listed by finding a whole or near whole coefficient.

You enter 2 then 3 and so on to find the 1st farthest string and so on within 30 and so on strings permutated. Each round gets harder and harder as the length of the number line gets bigger. So its hard to find more strings.

The purpose of the formula is based on a script that I written. The game is known as “Numberline” and the idea is to strike all the strings and show arithmetic work for human to understand.

The game gets exponentially more difficult as each number line grows in length with each new round.

You place all whole coefficients for Z on a number line. The more whole numbers you find by dividing the more the number line gets filled up. All strings are alphabetically organized. So do not mistake this as the closest string problem.

**You place all whole coefficients for S on a number line**

(The reason being that you might not get a string if you have a non-whole number) The graph below shows to the lower right that when you enter 1 you get the first farthest string and enter 2 and so on. Integers that are near wholes are okay.)

To get an idea here’s a a list of permuated strings. The goal of the game is to find all numerically listed strings that have whole or near whole S and mark them on the number line paper.

` 01 aa 02 ab 03 ac 04 ad 05 ae 06 af `

etc ….. ag, ah, & az…

Shortened string with whole number list out of S .

15 ao – 15th letter o S/RT = 2

10 aj – 10th letter j S/RT = 3

03 ac – 3rd letter c S/RT = 10

**Overall, what is the quickest way to find all whole or near-whole numbers solutions on any number-line of S size?**